s467
Batuhan SAYLAM
2023-12-30
library(ggplot2)
library(psych)
library(hexbin)
library(GGally)
library(tidyverse)
library(effectsize)
library(MVA)
library(MASS)
library(reshape2)
library(gridExtra)
library(grid)
library(car)
library(robustbase)
library(MVN)
library(ICSNP)
library(mvdalab)
library(rstatix)
library(heplots)EXPLORATORY DATA ANALYSIS
set.seed(467)
data=read.csv("C:/Users/ASUS/Desktop/stat467project/Life-Expectancy-Data-Updated.csv")
data["Region"]=as.factor(data$Region)
data["Country"]=as.factor(data$Country)
data2=subset(data, select = -c(Economy_status_Developed,Economy_status_Developing))
data3=subset(data, select = c(Economy_status_Developed,Economy_status_Developing))
data=cbind(data2,
Economy_status = apply(data3, 1,
function(x) names(x)[as.logical(as.numeric(
as.character(x)))]))
data["Economy_status"]=as.factor(data$Economy_status)
data["Hepatitis_B"]=as.numeric(data$Hepatitis_B)
data["Measles"]=as.numeric(data$Measles)
data["Polio"]=as.numeric(data$Polio)
data["Diphtheria"]=as.numeric(data$Diphtheria)
data["GDP_per_capita"]=as.numeric(data$GDP_per_capita)
data <- data[data["Year"]==2015, ]
data=subset(data,select = -Year)
data=na.omit(data)
str(data)## 'data.frame': 179 obs. of 19 variables:
## $ Country : Factor w/ 179 levels "Afghanistan",..: 165 149 134 30 61 3 123 98 122 176 ...
## $ Region : Factor w/ 9 levels "Africa","Asia",..: 5 4 8 1 1 1 5 1 8 2 ...
## $ Infant_deaths : num 11.1 2.7 6.6 57 39.7 21.6 9.6 41.3 2.2 17.4 ...
## $ Under_five_deaths : num 13 3.3 8.2 88 59.8 25.2 11.2 59 2.7 21.8 ...
## $ Adult_mortality : num 105.8 57.9 223 340.1 261.7 ...
## $ Alcohol_consumption : num 1.32 10.35 8.06 4.55 2.69 ...
## $ Hepatitis_B : num 97 97 97 84 97 95 99 69 88 97 ...
## $ Measles : num 65 94 97 64 64 99 98 64 91 65 ...
## $ BMI : num 27.8 26 26.2 24.3 23.9 25.5 26.3 21.3 26.6 21.7 ...
## $ Polio : num 97 97 97 77 96 95 99 68 95 97 ...
## $ Diphtheria : num 97 97 97 84 97 95 99 69 95 97 ...
## $ Incidents_HIV : num 0.08 0.09 0.08 1.12 0.96 0.05 0.05 0.24 0.04 0.12 ...
## $ GDP_per_capita : num 11006 25742 9313 1383 661 ...
## $ Population_mln : num 78.53 46.44 144.1 23.3 2.09 ...
## $ Thinness_ten_nineteen_years: num 4.9 0.6 2.3 5.6 7.3 6 7.1 7.1 0.8 14.2 ...
## $ Thinness_five_nine_years : num 4.8 0.5 2.3 5.5 7.2 5.8 6.9 7.1 0.7 14.5 ...
## $ Schooling : num 7.8 9.7 12 6.1 3.4 7.9 9.5 6.1 12.5 8 ...
## $ Life_expectancy : num 76.5 82.8 71.2 57.6 60.9 76.1 76.9 65.5 82.3 75.1 ...
## $ Economy_status : Factor w/ 2 levels "Economy_status_Developed",..: 2 1 2 2 2 2 2 2 1 2 ...summary(data)## Country Region Infant_deaths
## Afghanistan : 1 Africa :51 Min. : 1.80
## Albania : 1 Asia :27 1st Qu.: 6.65
## Algeria : 1 European Union :27 Median :15.20
## Angola : 1 Central America and Caribbean:19 Mean :23.56
## Antigua and Barbuda: 1 Rest of Europe :15 3rd Qu.:36.55
## Argentina : 1 Middle East :14 Max. :95.10
## (Other) :173 (Other) :26
## Under_five_deaths Adult_mortality Alcohol_consumption Hepatitis_B
## Min. : 2.30 Min. : 49.38 Min. : 0.000 Min. :22.0
## 1st Qu.: 7.85 1st Qu.: 90.79 1st Qu.: 1.360 1st Qu.:82.5
## Median : 17.50 Median :146.52 Median : 4.040 Median :92.0
## Mean : 31.68 Mean :163.67 Mean : 4.729 Mean :87.1
## 3rd Qu.: 49.95 3rd Qu.:215.65 3rd Qu.: 7.760 3rd Qu.:97.0
## Max. :140.20 Max. :513.48 Max. :16.720 Max. :99.0
##
## Measles BMI Polio Diphtheria
## Min. :21.00 Min. :20.5 Min. :37.00 Min. :16.00
## 1st Qu.:64.00 1st Qu.:23.8 1st Qu.:85.00 1st Qu.:85.50
## Median :84.00 Median :26.2 Median :93.00 Median :93.00
## Mean :80.23 Mean :25.6 Mean :88.26 Mean :87.92
## 3rd Qu.:94.00 3rd Qu.:27.0 3rd Qu.:97.00 3rd Qu.:97.00
## Max. :99.00 Max. :32.1 Max. :99.00 Max. :99.00
##
## Incidents_HIV GDP_per_capita Population_mln
## Min. : 0.0100 Min. : 306 Min. : 0.090
## 1st Qu.: 0.0800 1st Qu.: 1690 1st Qu.: 2.215
## Median : 0.1400 Median : 5391 Median : 9.110
## Mean : 0.6098 Mean : 12617 Mean : 40.088
## 3rd Qu.: 0.3700 3rd Qu.: 14274 3rd Qu.: 27.445
## Max. :14.3000 Max. :105462 Max. :1379.860
##
## Thinness_ten_nineteen_years Thinness_five_nine_years Schooling
## Min. : 0.10 Min. : 0.100 Min. : 1.400
## 1st Qu.: 1.50 1st Qu.: 1.500 1st Qu.: 5.950
## Median : 3.50 Median : 3.400 Median : 8.700
## Mean : 4.55 Mean : 4.594 Mean : 8.361
## 3rd Qu.: 6.50 3rd Qu.: 6.450 3rd Qu.:11.050
## Max. :26.70 Max. :27.300 Max. :14.100
##
## Life_expectancy Economy_status
## Min. :50.90 Economy_status_Developed : 37
## 1st Qu.:66.30 Economy_status_Developing:142
## Median :73.00
## Mean :71.46
## 3rd Qu.:76.85
## Max. :83.80
## head(data)## Country Region Infant_deaths Under_five_deaths
## 1 Turkiye Middle East 11.1 13.0
## 2 Spain European Union 2.7 3.3
## 7 Russian Federation Rest of Europe 6.6 8.2
## 28 Cameroon Africa 57.0 88.0
## 44 Gambia, The Africa 39.7 59.8
## 58 Algeria Africa 21.6 25.2
## Adult_mortality Alcohol_consumption Hepatitis_B Measles BMI Polio
## 1 105.8240 1.32 97 65 27.8 97
## 2 57.9025 10.35 97 94 26.0 97
## 7 223.0000 8.06 97 97 26.2 97
## 28 340.1265 4.55 84 64 24.3 77
## 44 261.7065 2.69 97 64 23.9 96
## 58 95.8155 0.55 95 99 25.5 95
## Diphtheria Incidents_HIV GDP_per_capita Population_mln
## 1 97 0.08 11006 78.53
## 2 97 0.09 25742 46.44
## 7 97 0.08 9313 144.10
## 28 84 1.12 1383 23.30
## 44 97 0.96 661 2.09
## 58 95 0.05 4178 39.73
## Thinness_ten_nineteen_years Thinness_five_nine_years Schooling
## 1 4.9 4.8 7.8
## 2 0.6 0.5 9.7
## 7 2.3 2.3 12.0
## 28 5.6 5.5 6.1
## 44 7.3 7.2 3.4
## 58 6.0 5.8 7.9
## Life_expectancy Economy_status
## 1 76.5 Economy_status_Developing
## 2 82.8 Economy_status_Developed
## 7 71.2 Economy_status_Developing
## 28 57.6 Economy_status_Developing
## 44 60.9 Economy_status_Developing
## 58 76.1 Economy_status_Developingdata2=subset(data,select = -c(Region,Country,Economy_status))cormat <- round(cor(data2),2)get_upper_tri <- function(cormat){
cormat[lower.tri(cormat)]<- NA
return(cormat)
}reorder_cormat <- function(cormat){
# Use correlation between variables as distance
dd <- as.dist((1-cormat)/2)
hc <- hclust(dd)
cormat <-cormat[hc$order, hc$order]
}cormat <- reorder_cormat(cormat)
upper_tri <- get_upper_tri(cormat)
melted_cormat <- melt(upper_tri, na.rm = TRUE)ggplot(melted_cormat, aes(Var2, Var1, fill = value))+
geom_tile(color = "white")+
scale_fill_gradient2(low = "blue", high = "red", mid = "white",
midpoint = 0, limit = c(-1,1), space = "Lab",
name="Pearson\nCorrelation") +
theme_minimal()+ # minimal theme
theme(axis.text.x = element_text(angle = 45, vjust = 1,
size = 12, hjust = 1))+
coord_fixed()+
geom_text(aes(Var2, Var1, label = value), color = "black", size = 3) +
theme(
axis.text.x=element_blank(),
axis.title.x = element_blank(),
axis.title.y = element_blank(),
panel.grid.major = element_blank(),
panel.border = element_blank(),
panel.background = element_blank(),
axis.ticks = element_blank(),
legend.justification = c(1, 0),
legend.position = c(0.6, 0.7),
legend.direction = "horizontal")+
guides(fill = guide_colorbar(barwidth = 7, barheight = 1,
title.position = "top", title.hjust = 0.5))
mvn(data2,multivariatePlot= "qq")$plot
## NULLThe variables which violates the multivariate normality since there
are large deviations from the line
result <- mvn(data = data2, mvnTest = "royston")
result$multivariateNormality## Test H p value MVN
## 1 Royston 342.1765 2.013471e-70 NOSince p-value is smaller than 0.05, we can reject the null hypthosis
which is that the data follows normal distribution
qqplots = lapply(1:ncol(data2), function(.x) ggplot(data2,aes(sample=as.numeric(unlist(data2[,.x]))))+stat_qq()+stat_qq_line()+ theme_classic() +ggtitle(colnames(data2)[.x]))
require(gridExtra)
do.call(grid.arrange, qqplots)
hplots = lapply(1:ncol(data2), function(.x) ggplot(data2,aes(x=unlist(data2[,colnames(data2)[.x]])))+geom_histogram(aes(y=..density..), colour="black", fill="white")+geom_density(alpha=.5, fill="darkblue")+ theme_classic()+labs(x=colnames(data2)[.x])+ggtitle(colnames(data2)[.x]))
require(gridExtra)
do.call(grid.arrange, hplots)
As you see, the variables which violates the multivariate normality.
# create univariate histograms
result <- mvn(data = data2, mvnTest = "royston", univariateTest = "SW" )
result$univariateNormality ## Test Variable Statistic p value Normality
## 1 Shapiro-Wilk Infant_deaths 0.8612 <0.001 NO
## 2 Shapiro-Wilk Under_five_deaths 0.8187 <0.001 NO
## 3 Shapiro-Wilk Adult_mortality 0.9202 <0.001 NO
## 4 Shapiro-Wilk Alcohol_consumption 0.9335 <0.001 NO
## 5 Shapiro-Wilk Hepatitis_B 0.7746 <0.001 NO
## 6 Shapiro-Wilk Measles 0.8876 <0.001 NO
## 7 Shapiro-Wilk BMI 0.9698 6e-04 NO
## 8 Shapiro-Wilk Polio 0.7744 <0.001 NO
## 9 Shapiro-Wilk Diphtheria 0.7283 <0.001 NO
## 10 Shapiro-Wilk Incidents_HIV 0.3677 <0.001 NO
## 11 Shapiro-Wilk GDP_per_capita 0.6862 <0.001 NO
## 12 Shapiro-Wilk Population_mln 0.2339 <0.001 NO
## 13 Shapiro-Wilk Thinness_ten_nineteen_years 0.8216 <0.001 NO
## 14 Shapiro-Wilk Thinness_five_nine_years 0.8242 <0.001 NO
## 15 Shapiro-Wilk Schooling 0.9617 1e-04 NO
## 16 Shapiro-Wilk Life_expectancy 0.9528 <0.001 NOSince the all p-values are smaller than 0.05, the variables which
violates the multivariate normality.
result$Descriptives## n Mean Std.Dev Median Min
## Infant_deaths 179 2.355866e+01 21.487508 15.2000 1.800
## Under_five_deaths 179 3.168045e+01 32.217096 17.5000 2.300
## Adult_mortality 179 1.636676e+02 89.954470 146.5195 49.384
## Alcohol_consumption 179 4.728994e+00 3.743322 4.0400 0.000
## Hepatitis_B 179 8.710056e+01 14.167575 92.0000 22.000
## Measles 179 8.022905e+01 16.185999 84.0000 21.000
## BMI 179 2.559609e+01 2.191669 26.2000 20.500
## Polio 179 8.826257e+01 13.024320 93.0000 37.000
## Diphtheria 179 8.791620e+01 14.693831 93.0000 16.000
## Incidents_HIV 179 6.097765e-01 1.621318 0.1400 0.010
## GDP_per_capita 179 1.261730e+04 17719.612926 5391.0000 306.000
## Population_mln 179 4.008793e+01 146.506422 9.1100 0.090
## Thinness_ten_nineteen_years 179 4.549721e+00 4.115992 3.5000 0.100
## Thinness_five_nine_years 179 4.593855e+00 4.195546 3.4000 0.100
## Schooling 179 8.360894e+00 3.146986 8.7000 1.400
## Life_expectancy 179 7.146369e+01 7.832270 73.0000 50.900
## Max 25th 75th Skew
## Infant_deaths 95.1000 6.65000 36.5500 1.12850717
## Under_five_deaths 140.2000 7.85000 49.9500 1.35663447
## Adult_mortality 513.4755 90.78575 215.6492 1.04384225
## Alcohol_consumption 16.7200 1.36000 7.7600 0.48900835
## Hepatitis_B 99.0000 82.50000 97.0000 -1.88604401
## Measles 99.0000 64.00000 94.0000 -0.84526412
## BMI 32.1000 23.80000 27.0000 -0.08139383
## Polio 99.0000 85.00000 97.0000 -1.79562345
## Diphtheria 99.0000 85.50000 97.0000 -2.19634211
## Incidents_HIV 14.3000 0.08000 0.3700 5.32064829
## GDP_per_capita 105462.0000 1690.00000 14274.5000 2.30984461
## Population_mln 1379.8600 2.21500 27.4450 7.98900304
## Thinness_ten_nineteen_years 26.7000 1.50000 6.5000 1.91176983
## Thinness_five_nine_years 27.3000 1.50000 6.4500 1.92769092
## Schooling 14.1000 5.95000 11.0500 -0.27144789
## Life_expectancy 83.8000 66.30000 76.8500 -0.59113627
## Kurtosis
## Infant_deaths 0.4568213
## Under_five_deaths 1.0935217
## Adult_mortality 0.9966979
## Alcohol_consumption -0.6896498
## Hepatitis_B 3.6237679
## Measles 0.3260768
## BMI -0.1759413
## Polio 2.9408103
## Diphtheria 5.4145578
## Incidents_HIV 34.3579078
## GDP_per_capita 5.8912927
## Population_mln 67.7536827
## Thinness_ten_nineteen_years 5.3396564
## Thinness_five_nine_years 5.4675130
## Schooling -1.0221789
## Life_expectancy -0.4306512Bivariate<-matrix(rep(0,36),(ncol(data2)*(ncol(data2)-1)),3)
for (i in 1:(ncol(data2)-1)){
for (j in (i+1):ncol(data2)){
Bivariate[(i*j),1:2]<-names(data2[,c(i,j)])
Bivariate[(i*j),3]<-mvn(data = data2[,c(i,j)], mvnTest = "royston", univariateTest = "SW")$multivariateNormality[,4]
}}
for(i in 1:nrow(Bivariate)){
if(Bivariate[i,3]=="0"){
Bivariate[i,3]=NA
}
}
Bivariate=na.omit(Bivariate)
Bivariate## [,1] [,2] [,3]
## [1,] "Infant_deaths" "Under_five_deaths" "NO"
## [2,] "Infant_deaths" "Adult_mortality" "NO"
## [3,] "Infant_deaths" "Alcohol_consumption" "NO"
## [4,] "Infant_deaths" "Hepatitis_B" "NO"
## [5,] "Under_five_deaths" "Adult_mortality" "NO"
## [6,] "Infant_deaths" "BMI" "NO"
## [7,] "Under_five_deaths" "Alcohol_consumption" "NO"
## [8,] "Infant_deaths" "Diphtheria" "NO"
## [9,] "Under_five_deaths" "Hepatitis_B" "NO"
## [10,] "Infant_deaths" "GDP_per_capita" "NO"
## [11,] "Adult_mortality" "Alcohol_consumption" "NO"
## [12,] "Infant_deaths" "Thinness_ten_nineteen_years" "NO"
## [13,] "Under_five_deaths" "BMI" "NO"
## [14,] "Adult_mortality" "Hepatitis_B" "NO"
## [15,] "Under_five_deaths" "Polio" "NO"
## [16,] "Adult_mortality" "Measles" "NO"
## [17,] "Alcohol_consumption" "Hepatitis_B" "NO"
## [18,] "Adult_mortality" "BMI" "NO"
## [19,] "Under_five_deaths" "GDP_per_capita" "NO"
## [20,] "Alcohol_consumption" "Measles" "NO"
## [21,] "Under_five_deaths" "Thinness_ten_nineteen_years" "NO"
## [22,] "Adult_mortality" "Diphtheria" "NO"
## [23,] "Alcohol_consumption" "BMI" "NO"
## [24,] "Hepatitis_B" "Measles" "NO"
## [25,] "Alcohol_consumption" "Polio" "NO"
## [26,] "Adult_mortality" "GDP_per_capita" "NO"
## [27,] "Hepatitis_B" "BMI" "NO"
## [28,] "Alcohol_consumption" "Diphtheria" "NO"
## [29,] "Adult_mortality" "Thinness_ten_nineteen_years" "NO"
## [30,] "Hepatitis_B" "Polio" "NO"
## [31,] "Measles" "BMI" "NO"
## [32,] "Alcohol_consumption" "GDP_per_capita" "NO"
## [33,] "Hepatitis_B" "Diphtheria" "NO"
## [34,] "Measles" "Polio" "NO"
## [35,] "Hepatitis_B" "Incidents_HIV" "NO"
## [36,] "Alcohol_consumption" "Thinness_ten_nineteen_years" "NO"
## [37,] "Measles" "Diphtheria" "NO"
## [38,] "Hepatitis_B" "GDP_per_capita" "NO"
## [39,] "BMI" "Polio" "NO"
## [40,] "Measles" "Incidents_HIV" "NO"
## [41,] "BMI" "Diphtheria" "NO"
## [42,] "Alcohol_consumption" "Life_expectancy" "NO"
## [43,] "Hepatitis_B" "Thinness_ten_nineteen_years" "NO"
## [44,] "Measles" "GDP_per_capita" "NO"
## [45,] "BMI" "Incidents_HIV" "NO"
## [46,] "Polio" "Diphtheria" "NO"
## [47,] "Hepatitis_B" "Schooling" "NO"
## [48,] "BMI" "GDP_per_capita" "NO"
## [49,] "Measles" "Thinness_ten_nineteen_years" "NO"
## [50,] "Polio" "Incidents_HIV" "NO"
## [51,] "BMI" "Population_mln" "NO"
## [52,] "Polio" "GDP_per_capita" "NO"
## [53,] "Diphtheria" "Incidents_HIV" "NO"
## [54,] "BMI" "Thinness_ten_nineteen_years" "NO"
## [55,] "Polio" "Population_mln" "NO"
## [56,] "BMI" "Thinness_five_nine_years" "NO"
## [57,] "Diphtheria" "GDP_per_capita" "NO"
## [58,] "Polio" "Thinness_ten_nineteen_years" "NO"
## [59,] "BMI" "Schooling" "NO"
## [60,] "Diphtheria" "Population_mln" "NO"
## [61,] "Incidents_HIV" "GDP_per_capita" "NO"
## [62,] "Polio" "Thinness_five_nine_years" "NO"
## [63,] "Diphtheria" "Thinness_ten_nineteen_years" "NO"
## [64,] "Incidents_HIV" "Population_mln" "NO"
## [65,] "Diphtheria" "Thinness_five_nine_years" "NO"
## [66,] "Polio" "Life_expectancy" "NO"
## [67,] "Incidents_HIV" "Thinness_ten_nineteen_years" "NO"
## [68,] "GDP_per_capita" "Population_mln" "NO"
## [69,] "Diphtheria" "Schooling" "NO"
## [70,] "Incidents_HIV" "Thinness_five_nine_years" "NO"
## [71,] "GDP_per_capita" "Thinness_ten_nineteen_years" "NO"
## [72,] "Diphtheria" "Life_expectancy" "NO"
## [73,] "Incidents_HIV" "Schooling" "NO"
## [74,] "GDP_per_capita" "Thinness_five_nine_years" "NO"
## [75,] "Population_mln" "Thinness_ten_nineteen_years" "NO"
## [76,] "Incidents_HIV" "Life_expectancy" "NO"
## [77,] "GDP_per_capita" "Schooling" "NO"
## [78,] "Population_mln" "Thinness_five_nine_years" "NO"
## [79,] "GDP_per_capita" "Life_expectancy" "NO"
## [80,] "Population_mln" "Schooling" "NO"
## [81,] "Thinness_ten_nineteen_years" "Thinness_five_nine_years" "NO"
## [82,] "Population_mln" "Life_expectancy" "NO"
## [83,] "Thinness_ten_nineteen_years" "Schooling" "NO"
## [84,] "Thinness_ten_nineteen_years" "Life_expectancy" "NO"
## [85,] "Thinness_five_nine_years" "Schooling" "NO"
## [86,] "Thinness_five_nine_years" "Life_expectancy" "NO"
## [87,] "Schooling" "Life_expectancy" "NO"
## attr(,"na.action")
## [1] 1 17 19 23 25 29 31 34 37 38 41 43 46 47 49 51 53 57
## [19] 58 59 61 62 67 68 69 71 73 74 76 79 81 82 83 85 86 87
## [37] 89 92 93 94 95 97 100 101 102 103 106 107 109 111 113 114 115 116
## [55] 118 119 121 122 123 124 125 127 129 131 133 134 136 137 138 139 141 142
## [73] 145 146 147 148 149 151 152 153 155 157 158 159 161 162 163 164 166 167
## [91] 169 170 171 172 173 174 175 177 178 179 181 183 184 185 186 187 188 189
## [109] 190 191 193 194 196 197 198 199 200 201 202 203 204 205 206 207 209 211
## [127] 212 213 214 215 216 217 218 219 220 221 222 223 225 226 227 228 229 230
## [145] 231 232 233 234 235 236 237 238 239
## attr(,"class")
## [1] "omit"In addition to the univarite non-normality of every variable,
bivariate non-normality also exhibits non-normality.
result <- mvn(data = data2, mvnTest = "royston", multivariateOutlierMethod = "quan")
As can be seen, this dataset contains 84 outlier observations that are proved by the Mahalanobis Distance.
result <- mvn(data = data2, mvnTest = "royston", multivariateOutlierMethod = "adj")
As can be seen, this dataset contains 80 outlier observations that are proved by the Adjusted Mahalanobis Distance.
One Population Mean
datatest=data[,c("Thinness_five_nine_years","Thinness_ten_nineteen_years")]mu0=c(4.5,4.5)
xbar = colMeans(datatest)
test<-mvn(datatest,mvnTest = "mardia")
test$multivariateNormality## Test Statistic p value Result
## 1 Mardia Skewness 2455.21532300756 0 NO
## 2 Mardia Kurtosis 138.82062093672 0 NO
## 3 MVN <NA> <NA> NOtest<-mvn(datatest,mvnTest = "mardia", univariateTest = "SW")
test$univariateNormality## Test Variable Statistic p value Normality
## 1 Shapiro-Wilk Thinness_five_nine_years 0.8242 <0.001 NO
## 2 Shapiro-Wilk Thinness_ten_nineteen_years 0.8216 <0.001 NOa=1
for(i in colnames(datatest)){
if(any(data[,i]<=0)){
next
}
else{
b <- boxcox(lm(as.numeric(unlist(datatest[,i]))~ 1))
lambda=b$x[which.max(b$y)]}
datatest[i] <- (as.numeric(unlist(datatest[,i]))^ lambda - 1) / lambda
mu0[a]=(mu0[a]^lambda-1)/lambda
a=a+1
}
test<-mvn(datatest,mvnTest = "mardia", univariateTest = "SW")
test$univariateNormality## Test Variable Statistic p value Normality
## 1 Shapiro-Wilk Thinness_five_nine_years 0.9879 0.1280 YES
## 2 Shapiro-Wilk Thinness_ten_nineteen_years 0.9859 0.0701 YESThe normality is satisfied. Let’s see our response matrix before we begin the formal tests.
error.bars (datatest, ylab="Group Means", xlab=" Dependent Variables")
mu0## [1] 1.785949 1.785949TF9 <- lm(Thinness_five_nine_years ~ 1, data = datatest)
confint(TF9)## 2.5 % 97.5 %
## (Intercept) 1.18284 1.562754TF19 <- lm(Thinness_ten_nineteen_years ~ 1, data = datatest)
confint(TF19)## 2.5 % 97.5 %
## (Intercept) 1.194447 1.562957As we have seen, the both CI do not include the mu0.
HotellingsT2(datatest,mu=mu0)##
## Hotelling's one sample T2-test
##
## data: datatest
## T.2 = 9.4836, df1 = 2, df2 = 177, p-value = 0.0001223
## alternative hypothesis: true location is not equal to c(1.78594895730098,1.78594895730098)Since p-value is smaller than 0.05, we reject H0. Therefore, we don’t have enough evidence to conclude that the transformation of the mean vector equals to transformation of (4.5,4.5).
MVcis(datatest)
## [,1] [,2]
## Thinness_five_nine_years 1.134499 1.611095
## Thinness_ten_nineteen_years 1.147557 1.609847mu0 values do not appear in the simultaneous confidence intervals for each variable because they do not fall inside the confidence region (that is, the point does not appear inside the ellipse), we reject the null hypothesis.
Two Independent Samples
datatest[,"Economy_status"]=data[,"Economy_status"]datatest %>% group_by(Economy_status) %>% shapiro_test(Thinness_five_nine_years
,Thinness_ten_nineteen_years)## # A tibble: 4 × 4
## Economy_status variable statistic p
## <fct> <chr> <dbl> <dbl>
## 1 Economy_status_Developed Thinness_five_nine_years 0.977 0.625
## 2 Economy_status_Developed Thinness_ten_nineteen_years 0.973 0.501
## 3 Economy_status_Developing Thinness_five_nine_years 0.972 0.00493
## 4 Economy_status_Developing Thinness_ten_nineteen_years 0.974 0.00839datanondev=datatest[datatest["Economy_status"]=="Economy_status_Developing",c(1,2)]qqplots = lapply(1:ncol(datanondev), function(.x)
ggplot(datanondev,aes(sample=as.numeric(unlist(datanondev[,.x]))))+stat_qq()+stat_qq_line()+ theme_classic() +ggtitle(colnames(datanondev)[.x]))
require(gridExtra)
do.call(grid.arrange, qqplots)
# create univariate histograms
result <- mvn(data = datanondev, mvnTest = "royston", univariatePlot = "histogram", univariateTest = "SW" )
Although the p-value is significant for each combination of Economy_status_Developing, we can not reject null hypothesis because of visual inspection leading us to believe that the data is normal.
boxM(Y = cbind(datatest$Thinness_five_nine_years ,datatest$Thinness_ten_nineteen_years), group = factor(datatest$Economy_status))##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: cbind(datatest$Thinness_five_nine_years, datatest$Thinness_ten_nineteen_years)
## Chi-Sq (approx.) = 86.822, df = 3, p-value < 2.2e-16We reject the null hypothesis and come to the conclusion that
variance-covariance matrices are not equal for every combination of the
dependent variable created by each group in the independent variable
since the p-value for Box’s M test is significant.
Given that the assumption is false, it would be wise to use Levene’s
test to verify the homogeneity of variance assumption and determine
which variable fails in equal variance.
leveneTest(Thinness_five_nine_years ~ Economy_status, datatest)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 10.126 0.001727 **
## 177
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1leveneTest(Thinness_ten_nineteen_years ~ Economy_status, datatest)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 14.493 0.0001937 ***
## 177
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1According to Levene’s tests, both variable fail in equal variance.
HotellingsT2(cbind(datatest$Thinness_ten_nineteen_years,datatest$Thinness_five_nine_years) ~ datatest$Economy_status)##
## Hotelling's two sample T2-test
##
## data: cbind(datatest$Thinness_ten_nineteen_years, datatest$Thinness_five_nine_years) by datatest$Economy_status
## T.2 = 38.137, df1 = 2, df2 = 176, p-value = 1.732e-14
## alternative hypothesis: true location difference is not equal to c(0,0)We reject H0 since the p value is significant. As a result, we have sufficient evidence to prove that the economy has an impact on the mean of the responses.
#Simultaneous Confidence Intervals
xbar_0<-colMeans(datatest[datatest["Economy_status"]=="Economy_status_Developing",c(1,2)])
xbar_1<-colMeans(datatest[datatest["Economy_status"]=="Economy_status_Developed",c(1,2)])
n1<-dim(datatest[datatest["Economy_status"]=="Economy_status_Developing",])[1]
n2<-dim(datatest[datatest["Economy_status"]=="Economy_status_Developed",])[1]
p<-2
F<-qf(0.05, p, (n1+n2-p-1), lower.tail=FALSE)
c_square<-(((n1+n2-2)*p)/(n1+n2-p-1))*F
sd1<-sd(datatest$Thinness_five_nine_years)
sd2<-sd(datatest$Thinness_ten_nineteen_years)
LC1<-(xbar_0[1]-xbar_1[1])-sqrt(c_square)*sqrt((1/n1)+(1/n2))*sd1
UC1<-(xbar_0[1]-xbar_1[1])+sqrt(c_square)*sqrt((1/n1)+(1/n2))*sd1
SCI_1<-c(LC1, UC1)
LC2<-(xbar_0[2]-xbar_1[2])-sqrt(c_square)*sqrt((1/n1)+(1/n2))*sd1
UC2<-(xbar_0[2]-xbar_1[2])+sqrt(c_square)*sqrt((1/n1)+(1/n2))*sd1
SCI_2<-c(LC2, UC2)
#Bonferroni Confidence Intervals
m<-2
t<-qt(0.05/2*m, n1+n2-2, lower.tail=FALSE)
LC1<-(xbar_0[1]-xbar_1[1])-t*sqrt((1/n1)+(1/n2))*sd2
UC1<-(xbar_0[1]-xbar_1[1])+t*sqrt((1/n1)+(1/n2))*sd2
BCI_1<-c(LC1, UC1)
LC2<-(xbar_0[2]-xbar_1[2])-t*sqrt((1/n1)+(1/n2))*sd2
UC2<-(xbar_0[2]-xbar_1[2])+t*sqrt((1/n1)+(1/n2))*sd2
BCI_2<-c(LC2, UC2)
SCI_1 ## Thinness_five_nine_years Thinness_five_nine_years
## 1.155275 2.332301BCI_1 ## Thinness_five_nine_years Thinness_five_nine_years
## 1.362527 2.125050SCI_2 ## Thinness_ten_nineteen_years Thinness_ten_nineteen_years
## 1.051640 2.228666BCI_2 ## Thinness_ten_nineteen_years Thinness_ten_nineteen_years
## 1.258891 2.021414Bonferroni confidence intervals give narrower intervals and both CI for Thinness_ten_nineteen_years and Thinness_five_nine_years.However, any of them does not include 0.
One Way MANOVA
dataowa=datatest[,c("Thinness_five_nine_years","Thinness_ten_nineteen_years")]
dataowa["Region"]=data[,"Region"]
dataowa## Thinness_five_nine_years Thinness_ten_nineteen_years
## 1 1.87675095 1.90603667
## 2 -0.64240208 -0.48289863
## 7 0.91497527 0.91497527
## 28 2.07260535 2.09897556
## 44 2.47799809 2.49941974
## 58 2.15063600 2.20092896
## 75 2.41231344 2.45634377
## 102 2.45634377 2.45634377
## 111 -0.34290589 -0.21770132
## 113 3.65256541 3.61477701
## 122 1.65724882 1.62355500
## 161 2.22558793 2.29772543
## 167 0.80660548 0.86174855
## 174 3.84441782 3.79789609
## 183 2.88636810 2.92137584
## 203 0.74938068 0.68988528
## 217 2.68260955 2.70198297
## 220 0.96643138 0.91497527
## 242 0.56318021 0.56318021
## 269 0.09632668 0.18606541
## 272 -1.05636402 -0.82902522
## 301 2.72117568 2.74019149
## 304 0.18606541 0.09632668
## 331 1.96324071 2.01872570
## 334 2.43445091 2.45634377
## 416 0.80660548 0.80660548
## 427 2.49941974 2.49941974
## 444 0.34937100 0.42429321
## 452 0.18606541 0.34937100
## 474 1.32730923 1.36729377
## 488 0.42429321 0.42429321
## 496 0.62790224 0.62790224
## 499 2.38992500 2.41231344
## 512 1.40634675 1.44451632
## 547 -1.80232087 -1.80232087
## 557 1.06453417 1.11139871
## 559 2.01872570 2.07260535
## 580 1.20121770 1.48184688
## 585 2.68260955 2.72117568
## 591 1.40634675 1.44451632
## 599 -0.64240208 -0.48289863
## 609 1.55415190 1.55415190
## 627 0.27016343 0.18606541
## 629 2.01872570 2.07260535
## 639 2.56234400 2.60322806
## 640 4.88339003 4.83716463
## 651 1.06453417 1.06453417
## 688 1.36729377 1.36729377
## 697 1.36729377 1.36729377
## 700 2.24993446 2.29772543
## 717 3.45711218 3.42974412
## 728 2.20092896 2.12498202
## 733 -0.10413666 0.00000000
## 741 2.47799809 2.49941974
## 764 1.44451632 1.48184688
## 766 0.62790224 0.68988528
## 770 2.49941974 2.52061436
## 787 2.22558793 2.27397746
## 810 0.42429321 0.49542577
## 811 0.62790224 0.68988528
## 833 1.62355500 1.62355500
## 838 2.32118654 2.36727900
## 840 2.17594824 2.22558793
## 850 1.20121770 1.15693209
## 852 2.95581497 2.97282781
## 853 2.58288928 2.58288928
## 869 0.91497527 0.86174855
## 874 -0.64240208 -0.34290589
## 901 3.53729759 3.53729759
## 903 2.32118654 2.36727900
## 904 2.17594824 2.12498202
## 907 1.96324071 2.01872570
## 957 2.09897556 2.09897556
## 1000 2.01872570 2.07260535
## 1011 4.21727064 4.17741892
## 1058 2.22558793 2.24993446
## 1064 -0.21770132 -0.10413666
## 1067 3.97878983 3.96787407
## 1068 1.40634675 1.44451632
## 1117 1.90603667 1.90603667
## 1146 0.27016343 0.34937100
## 1150 0.56318021 0.62790224
## 1157 0.00000000 0.00000000
## 1158 2.70198297 2.72117568
## 1164 1.51837942 1.55415190
## 1197 0.62790224 0.80660548
## 1205 0.80660548 0.80660548
## 1206 2.24993446 2.29772543
## 1225 0.18606541 0.18606541
## 1227 2.88636810 2.92137584
## 1251 1.72276330 1.72276330
## 1262 0.68988528 0.80660548
## 1266 1.51837942 1.48184688
## 1306 0.80660548 0.68988528
## 1320 1.15693209 1.11139871
## 1338 2.45634377 2.54158737
## 1358 2.66305150 2.68260955
## 1481 2.07260535 2.09897556
## 1492 -0.21770132 -0.21770132
## 1503 2.56234400 2.60322806
## 1531 0.62790224 0.62790224
## 1536 -0.34290589 -0.21770132
## 1559 0.09632668 0.18606541
## 1566 -1.35307896 -1.05636402
## 1588 0.34937100 0.42429321
## 1604 1.40634675 1.36729377
## 1614 -1.05636402 -0.82902522
## 1620 0.18606541 0.18606541
## 1624 1.90603667 1.99119070
## 1629 2.54158737 2.60322806
## 1707 3.51088038 3.53729759
## 1710 2.22558793 2.27397746
## 1713 1.01624602 0.96643138
## 1716 0.74938068 0.74938068
## 1722 0.68988528 0.74938068
## 1732 -1.35307896 -1.35307896
## 1785 0.91497527 0.91497527
## 1801 1.96324071 2.12498202
## 1810 -0.48289863 -0.21770132
## 1820 2.90394439 2.93866516
## 1824 0.86174855 0.80660548
## 1844 4.08533410 4.04327328
## 1875 2.29772543 2.34436857
## 1882 1.28634070 1.24433103
## 1905 0.34937100 0.42429321
## 1948 -0.21770132 -0.21770132
## 1950 0.09632668 0.09632668
## 1976 2.29772543 2.32118654
## 1984 -0.10413666 0.09632668
## 1989 2.12498202 2.12498202
## 2022 2.38992500 2.41231344
## 2077 0.27016343 0.27016343
## 2081 0.86174855 0.86174855
## 2118 2.75903410 2.74019149
## 2120 0.74938068 0.68988528
## 2127 -0.48289863 -0.48289863
## 2128 1.36729377 1.44451632
## 2146 0.09632668 0.09632668
## 2148 0.34937100 0.42429321
## 2178 0.68988528 0.68988528
## 2182 0.49542577 0.49542577
## 2235 2.68260955 2.68260955
## 2279 -0.48289863 -0.48289863
## 2281 1.15693209 1.15693209
## 2291 1.15693209 1.11139871
## 2322 1.01624602 1.01624602
## 2324 1.44451632 1.44451632
## 2325 -0.10413666 0.00000000
## 2339 2.07260535 2.15063600
## 2357 -0.48289863 -0.21770132
## 2368 -0.10413666 0.00000000
## 2379 3.83287241 3.76239602
## 2396 0.00000000 0.00000000
## 2405 2.34436857 2.34436857
## 2410 2.81455771 2.79621381
## 2443 -0.10413666 0.00000000
## 2449 2.24993446 2.32118654
## 2469 0.68988528 0.68988528
## 2496 2.95581497 0.00000000
## 2519 1.11139871 1.01624602
## 2526 1.58919952 1.58919952
## 2582 2.07260535 2.07260535
## 2618 2.54158737 2.64330473
## 2621 0.09632668 0.18606541
## 2642 3.18256970 0.68988528
## 2651 1.51837942 1.62355500
## 2662 2.54158737 2.58288928
## 2680 -1.80232087 -1.35307896
## 2702 3.71421615 3.72635394
## 2711 0.18606541 0.34937100
## 2713 -0.48289863 -0.34290589
## 2728 2.49941974 2.54158737
## 2738 -1.80232087 -1.80232087
## 2753 2.01872570 1.75463538
## 2754 2.29772543 2.32118654
## 2821 0.42429321 0.49542577
## 2841 2.04585955 2.09897556
## 2847 0.56318021 0.62790224
## 2849 2.22558793 2.24993446
## Region
## 1 Middle East
## 2 European Union
## 7 Rest of Europe
## 28 Africa
## 44 Africa
## 58 Africa
## 75 Middle East
## 102 Africa
## 111 Rest of Europe
## 113 Asia
## 122 Africa
## 161 Africa
## 167 European Union
## 174 Asia
## 183 Africa
## 203 Rest of Europe
## 217 Africa
## 220 Rest of Europe
## 242 Central America and Caribbean
## 269 Middle East
## 272 Oceania
## 301 Africa
## 304 Oceania
## 331 Middle East
## 334 Africa
## 416 Central America and Caribbean
## 427 Africa
## 444 European Union
## 452 Asia
## 474 Central America and Caribbean
## 488 North America
## 496 European Union
## 499 Africa
## 512 Central America and Caribbean
## 547 Oceania
## 557 South America
## 559 South America
## 580 Asia
## 585 Africa
## 591 Middle East
## 599 North America
## 609 Central America and Caribbean
## 627 Rest of Europe
## 629 Africa
## 639 Middle East
## 640 Asia
## 651 European Union
## 688 Asia
## 697 Central America and Caribbean
## 700 Africa
## 717 Asia
## 728 Africa
## 733 European Union
## 741 Africa
## 764 Africa
## 766 European Union
## 770 Africa
## 787 Middle East
## 810 Central America and Caribbean
## 811 Central America and Caribbean
## 833 Middle East
## 838 Africa
## 840 Africa
## 850 Asia
## 852 Africa
## 853 Asia
## 869 Asia
## 874 European Union
## 901 Asia
## 903 Africa
## 904 Central America and Caribbean
## 907 Middle East
## 957 Africa
## 1000 Central America and Caribbean
## 1011 Asia
## 1058 Africa
## 1064 European Union
## 1067 Asia
## 1068 Central America and Caribbean
## 1117 Middle East
## 1146 European Union
## 1150 Central America and Caribbean
## 1157 European Union
## 1158 Africa
## 1164 Central America and Caribbean
## 1197 Asia
## 1205 Rest of Europe
## 1206 Africa
## 1225 European Union
## 1227 Africa
## 1251 Central America and Caribbean
## 1262 South America
## 1266 Asia
## 1306 European Union
## 1320 Rest of Europe
## 1338 Africa
## 1358 Africa
## 1481 Africa
## 1492 European Union
## 1503 Africa
## 1531 Rest of Europe
## 1536 European Union
## 1559 South America
## 1566 European Union
## 1588 European Union
## 1604 Asia
## 1614 Rest of Europe
## 1620 Central America and Caribbean
## 1624 Middle East
## 1629 Africa
## 1707 Middle East
## 1710 Africa
## 1713 Asia
## 1716 Rest of Europe
## 1722 South America
## 1732 Oceania
## 1785 Rest of Europe
## 1801 Asia
## 1810 Rest of Europe
## 1820 Africa
## 1824 Rest of Europe
## 1844 Asia
## 1875 Africa
## 1882 Asia
## 1905 South America
## 1948 South America
## 1950 European Union
## 1976 Africa
## 1984 European Union
## 1989 Africa
## 2022 Africa
## 2077 Oceania
## 2081 Asia
## 2118 Middle East
## 2120 European Union
## 2127 European Union
## 2128 Central America and Caribbean
## 2146 South America
## 2148 Oceania
## 2178 Asia
## 2182 European Union
## 2235 Africa
## 2279 Oceania
## 2281 Africa
## 2291 Rest of Europe
## 2322 Central America and Caribbean
## 2324 South America
## 2325 European Union
## 2339 Africa
## 2357 North America
## 2368 South America
## 2379 Asia
## 2396 European Union
## 2405 Africa
## 2410 Asia
## 2443 Rest of Europe
## 2449 Africa
## 2469 European Union
## 2496 Asia
## 2519 European Union
## 2526 Central America and Caribbean
## 2582 Africa
## 2618 Africa
## 2621 South America
## 2642 Oceania
## 2651 Oceania
## 2662 Africa
## 2680 Oceania
## 2702 Asia
## 2711 Africa
## 2713 European Union
## 2728 Asia
## 2738 Oceania
## 2753 Africa
## 2754 Africa
## 2821 South America
## 2841 Africa
## 2847 Central America and Caribbean
## 2849 Middle Eastdataowa %>% group_by(Region) %>% summarise(n = n(),
mean_9 = mean(Thinness_five_nine_years),
sd_9 = sd(Thinness_five_nine_years),
mean_19 = mean(Thinness_ten_nineteen_years),
sd_19 = sd(Thinness_ten_nineteen_years))## # A tibble: 9 × 6
## Region n mean_9 sd_9 mean_19 sd_19
## <fct> <int> <dbl> <dbl> <dbl> <dbl>
## 1 Africa 51 2.29 0.455 2.32 0.452
## 2 Asia 27 2.38 1.38 2.28 1.42
## 3 Central America and Caribbean 19 1.17 0.566 1.19 0.556
## 4 European Union 27 0.131 0.589 0.191 0.516
## 5 Middle East 14 2.03 0.764 2.07 0.750
## 6 North America 3 -0.234 0.575 -0.0921 0.466
## 7 Oceania 11 -0.254 1.58 -0.411 1.12
## 8 Rest of Europe 15 0.479 0.671 0.505 0.580
## 9 South America 12 0.554 0.671 0.613 0.666p1 <- ggplot(dataowa, aes(x = Region, y = Thinness_five_nine_years, fill = Region)) + geom_boxplot(outlier.shape = NA) + geom_jitter(width = 0.2) + theme(legend.position="top")+theme_minimal()+
labs(title = "The Box Plot of Thinness_five_nine_years by Region" ,subtitle = "Transformed Thinness_five_nine_years.")
p2 <- ggplot(dataowa, aes(x = Region, y = Thinness_ten_nineteen_years, fill = Region)) + geom_boxplot(outlier.shape = NA) + geom_jitter(width = 0.2) + theme(legend.position="top")+theme_minimal()+
labs(title = "The Box Plot of Thinness_ten_nineteen_years by Region" ,subtitle = "Tranformed Thinness_ten_nineteen_years.")
grid.arrange(p1, p2, ncol=2) 
dataowa %>% group_by(Region) %>% shapiro_test(Thinness_five_nine_years,Thinness_ten_nineteen_years)## # A tibble: 18 × 4
## Region variable statistic p
## <fct> <chr> <dbl> <dbl>
## 1 Africa Thinness_five_nine_years 0.811 1.33e-6
## 2 Africa Thinness_ten_nineteen_years 0.839 6.51e-6
## 3 Asia Thinness_five_nine_years 0.922 4.32e-2
## 4 Asia Thinness_ten_nineteen_years 0.920 3.99e-2
## 5 Central America and Caribbean Thinness_five_nine_years 0.946 3.35e-1
## 6 Central America and Caribbean Thinness_ten_nineteen_years 0.940 2.68e-1
## 7 European Union Thinness_five_nine_years 0.973 6.92e-1
## 8 European Union Thinness_ten_nineteen_years 0.971 6.30e-1
## 9 Middle East Thinness_five_nine_years 0.913 1.74e-1
## 10 Middle East Thinness_ten_nineteen_years 0.920 2.19e-1
## 11 North America Thinness_five_nine_years 0.859 2.66e-1
## 12 North America Thinness_ten_nineteen_years 0.946 5.51e-1
## 13 Oceania Thinness_five_nine_years 0.887 1.28e-1
## 14 Oceania Thinness_ten_nineteen_years 0.941 5.37e-1
## 15 Rest of Europe Thinness_five_nine_years 0.847 1.58e-2
## 16 Rest of Europe Thinness_ten_nineteen_years 0.860 2.39e-2
## 17 South America Thinness_five_nine_years 0.906 1.88e-1
## 18 South America Thinness_ten_nineteen_years 0.927 3.47e-1dataowa2=dataowadataowa2 %>% group_by(Region) %>% shapiro_test(Thinness_five_nine_years,Thinness_ten_nineteen_years)## # A tibble: 18 × 4
## Region variable statistic p
## <fct> <chr> <dbl> <dbl>
## 1 Africa Thinness_five_nine_years 0.811 1.33e-6
## 2 Africa Thinness_ten_nineteen_years 0.839 6.51e-6
## 3 Asia Thinness_five_nine_years 0.922 4.32e-2
## 4 Asia Thinness_ten_nineteen_years 0.920 3.99e-2
## 5 Central America and Caribbean Thinness_five_nine_years 0.946 3.35e-1
## 6 Central America and Caribbean Thinness_ten_nineteen_years 0.940 2.68e-1
## 7 European Union Thinness_five_nine_years 0.973 6.92e-1
## 8 European Union Thinness_ten_nineteen_years 0.971 6.30e-1
## 9 Middle East Thinness_five_nine_years 0.913 1.74e-1
## 10 Middle East Thinness_ten_nineteen_years 0.920 2.19e-1
## 11 North America Thinness_five_nine_years 0.859 2.66e-1
## 12 North America Thinness_ten_nineteen_years 0.946 5.51e-1
## 13 Oceania Thinness_five_nine_years 0.887 1.28e-1
## 14 Oceania Thinness_ten_nineteen_years 0.941 5.37e-1
## 15 Rest of Europe Thinness_five_nine_years 0.847 1.58e-2
## 16 Rest of Europe Thinness_ten_nineteen_years 0.860 2.39e-2
## 17 South America Thinness_five_nine_years 0.906 1.88e-1
## 18 South America Thinness_ten_nineteen_years 0.927 3.47e-1boxM(Y = cbind(dataowa2$Thinness_five_nine_years,dataowa2$Thinness_ten_nineteen_years), group = factor(dataowa2$Region))##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: cbind(dataowa2$Thinness_five_nine_years, dataowa2$Thinness_ten_nineteen_years)
## Chi-Sq (approx.) = 453.64, df = 24, p-value < 2.2e-16leveneTest(Thinness_ten_nineteen_years ~ Region, dataowa2)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 8 12.91 1.878e-14 ***
## 170
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1leveneTest(Thinness_five_nine_years ~ Region, dataowa2)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 8 11.044 1.668e-12 ***
## 170
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1m1 <- manova(cbind(Thinness_five_nine_years,Thinness_ten_nineteen_years) ~ Region, data = dataowa2)
summary(m1)## Df Pillai approx F num Df den Df Pr(>F)
## Region 8 0.67122 10.734 16 340 < 2.2e-16 ***
## Residuals 170
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary.aov(m1)## Response Thinness_five_nine_years :
## Df Sum Sq Mean Sq F value Pr(>F)
## Region 8 175.96 21.9951 31.35 < 2.2e-16 ***
## Residuals 170 119.27 0.7016
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Response Thinness_ten_nineteen_years :
## Df Sum Sq Mean Sq F value Pr(>F)
## Region 8 172.66 21.5830 34.908 < 2.2e-16 ***
## Residuals 170 105.11 0.6183
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Two-Way MANOVA
datatwa=cbind(dataowa,data["Economy_status"])
datatwa## Thinness_five_nine_years Thinness_ten_nineteen_years
## 1 1.87675095 1.90603667
## 2 -0.64240208 -0.48289863
## 7 0.91497527 0.91497527
## 28 2.07260535 2.09897556
## 44 2.47799809 2.49941974
## 58 2.15063600 2.20092896
## 75 2.41231344 2.45634377
## 102 2.45634377 2.45634377
## 111 -0.34290589 -0.21770132
## 113 3.65256541 3.61477701
## 122 1.65724882 1.62355500
## 161 2.22558793 2.29772543
## 167 0.80660548 0.86174855
## 174 3.84441782 3.79789609
## 183 2.88636810 2.92137584
## 203 0.74938068 0.68988528
## 217 2.68260955 2.70198297
## 220 0.96643138 0.91497527
## 242 0.56318021 0.56318021
## 269 0.09632668 0.18606541
## 272 -1.05636402 -0.82902522
## 301 2.72117568 2.74019149
## 304 0.18606541 0.09632668
## 331 1.96324071 2.01872570
## 334 2.43445091 2.45634377
## 416 0.80660548 0.80660548
## 427 2.49941974 2.49941974
## 444 0.34937100 0.42429321
## 452 0.18606541 0.34937100
## 474 1.32730923 1.36729377
## 488 0.42429321 0.42429321
## 496 0.62790224 0.62790224
## 499 2.38992500 2.41231344
## 512 1.40634675 1.44451632
## 547 -1.80232087 -1.80232087
## 557 1.06453417 1.11139871
## 559 2.01872570 2.07260535
## 580 1.20121770 1.48184688
## 585 2.68260955 2.72117568
## 591 1.40634675 1.44451632
## 599 -0.64240208 -0.48289863
## 609 1.55415190 1.55415190
## 627 0.27016343 0.18606541
## 629 2.01872570 2.07260535
## 639 2.56234400 2.60322806
## 640 4.88339003 4.83716463
## 651 1.06453417 1.06453417
## 688 1.36729377 1.36729377
## 697 1.36729377 1.36729377
## 700 2.24993446 2.29772543
## 717 3.45711218 3.42974412
## 728 2.20092896 2.12498202
## 733 -0.10413666 0.00000000
## 741 2.47799809 2.49941974
## 764 1.44451632 1.48184688
## 766 0.62790224 0.68988528
## 770 2.49941974 2.52061436
## 787 2.22558793 2.27397746
## 810 0.42429321 0.49542577
## 811 0.62790224 0.68988528
## 833 1.62355500 1.62355500
## 838 2.32118654 2.36727900
## 840 2.17594824 2.22558793
## 850 1.20121770 1.15693209
## 852 2.95581497 2.97282781
## 853 2.58288928 2.58288928
## 869 0.91497527 0.86174855
## 874 -0.64240208 -0.34290589
## 901 3.53729759 3.53729759
## 903 2.32118654 2.36727900
## 904 2.17594824 2.12498202
## 907 1.96324071 2.01872570
## 957 2.09897556 2.09897556
## 1000 2.01872570 2.07260535
## 1011 4.21727064 4.17741892
## 1058 2.22558793 2.24993446
## 1064 -0.21770132 -0.10413666
## 1067 3.97878983 3.96787407
## 1068 1.40634675 1.44451632
## 1117 1.90603667 1.90603667
## 1146 0.27016343 0.34937100
## 1150 0.56318021 0.62790224
## 1157 0.00000000 0.00000000
## 1158 2.70198297 2.72117568
## 1164 1.51837942 1.55415190
## 1197 0.62790224 0.80660548
## 1205 0.80660548 0.80660548
## 1206 2.24993446 2.29772543
## 1225 0.18606541 0.18606541
## 1227 2.88636810 2.92137584
## 1251 1.72276330 1.72276330
## 1262 0.68988528 0.80660548
## 1266 1.51837942 1.48184688
## 1306 0.80660548 0.68988528
## 1320 1.15693209 1.11139871
## 1338 2.45634377 2.54158737
## 1358 2.66305150 2.68260955
## 1481 2.07260535 2.09897556
## 1492 -0.21770132 -0.21770132
## 1503 2.56234400 2.60322806
## 1531 0.62790224 0.62790224
## 1536 -0.34290589 -0.21770132
## 1559 0.09632668 0.18606541
## 1566 -1.35307896 -1.05636402
## 1588 0.34937100 0.42429321
## 1604 1.40634675 1.36729377
## 1614 -1.05636402 -0.82902522
## 1620 0.18606541 0.18606541
## 1624 1.90603667 1.99119070
## 1629 2.54158737 2.60322806
## 1707 3.51088038 3.53729759
## 1710 2.22558793 2.27397746
## 1713 1.01624602 0.96643138
## 1716 0.74938068 0.74938068
## 1722 0.68988528 0.74938068
## 1732 -1.35307896 -1.35307896
## 1785 0.91497527 0.91497527
## 1801 1.96324071 2.12498202
## 1810 -0.48289863 -0.21770132
## 1820 2.90394439 2.93866516
## 1824 0.86174855 0.80660548
## 1844 4.08533410 4.04327328
## 1875 2.29772543 2.34436857
## 1882 1.28634070 1.24433103
## 1905 0.34937100 0.42429321
## 1948 -0.21770132 -0.21770132
## 1950 0.09632668 0.09632668
## 1976 2.29772543 2.32118654
## 1984 -0.10413666 0.09632668
## 1989 2.12498202 2.12498202
## 2022 2.38992500 2.41231344
## 2077 0.27016343 0.27016343
## 2081 0.86174855 0.86174855
## 2118 2.75903410 2.74019149
## 2120 0.74938068 0.68988528
## 2127 -0.48289863 -0.48289863
## 2128 1.36729377 1.44451632
## 2146 0.09632668 0.09632668
## 2148 0.34937100 0.42429321
## 2178 0.68988528 0.68988528
## 2182 0.49542577 0.49542577
## 2235 2.68260955 2.68260955
## 2279 -0.48289863 -0.48289863
## 2281 1.15693209 1.15693209
## 2291 1.15693209 1.11139871
## 2322 1.01624602 1.01624602
## 2324 1.44451632 1.44451632
## 2325 -0.10413666 0.00000000
## 2339 2.07260535 2.15063600
## 2357 -0.48289863 -0.21770132
## 2368 -0.10413666 0.00000000
## 2379 3.83287241 3.76239602
## 2396 0.00000000 0.00000000
## 2405 2.34436857 2.34436857
## 2410 2.81455771 2.79621381
## 2443 -0.10413666 0.00000000
## 2449 2.24993446 2.32118654
## 2469 0.68988528 0.68988528
## 2496 2.95581497 0.00000000
## 2519 1.11139871 1.01624602
## 2526 1.58919952 1.58919952
## 2582 2.07260535 2.07260535
## 2618 2.54158737 2.64330473
## 2621 0.09632668 0.18606541
## 2642 3.18256970 0.68988528
## 2651 1.51837942 1.62355500
## 2662 2.54158737 2.58288928
## 2680 -1.80232087 -1.35307896
## 2702 3.71421615 3.72635394
## 2711 0.18606541 0.34937100
## 2713 -0.48289863 -0.34290589
## 2728 2.49941974 2.54158737
## 2738 -1.80232087 -1.80232087
## 2753 2.01872570 1.75463538
## 2754 2.29772543 2.32118654
## 2821 0.42429321 0.49542577
## 2841 2.04585955 2.09897556
## 2847 0.56318021 0.62790224
## 2849 2.22558793 2.24993446
## Region Economy_status
## 1 Middle East Economy_status_Developing
## 2 European Union Economy_status_Developed
## 7 Rest of Europe Economy_status_Developing
## 28 Africa Economy_status_Developing
## 44 Africa Economy_status_Developing
## 58 Africa Economy_status_Developing
## 75 Middle East Economy_status_Developing
## 102 Africa Economy_status_Developing
## 111 Rest of Europe Economy_status_Developed
## 113 Asia Economy_status_Developing
## 122 Africa Economy_status_Developing
## 161 Africa Economy_status_Developing
## 167 European Union Economy_status_Developed
## 174 Asia Economy_status_Developing
## 183 Africa Economy_status_Developing
## 203 Rest of Europe Economy_status_Developing
## 217 Africa Economy_status_Developing
## 220 Rest of Europe Economy_status_Developing
## 242 Central America and Caribbean Economy_status_Developing
## 269 Middle East Economy_status_Developed
## 272 Oceania Economy_status_Developed
## 301 Africa Economy_status_Developing
## 304 Oceania Economy_status_Developing
## 331 Middle East Economy_status_Developing
## 334 Africa Economy_status_Developing
## 416 Central America and Caribbean Economy_status_Developing
## 427 Africa Economy_status_Developing
## 444 European Union Economy_status_Developed
## 452 Asia Economy_status_Developing
## 474 Central America and Caribbean Economy_status_Developing
## 488 North America Economy_status_Developing
## 496 European Union Economy_status_Developed
## 499 Africa Economy_status_Developing
## 512 Central America and Caribbean Economy_status_Developing
## 547 Oceania Economy_status_Developing
## 557 South America Economy_status_Developing
## 559 South America Economy_status_Developing
## 580 Asia Economy_status_Developing
## 585 Africa Economy_status_Developing
## 591 Middle East Economy_status_Developing
## 599 North America Economy_status_Developed
## 609 Central America and Caribbean Economy_status_Developing
## 627 Rest of Europe Economy_status_Developing
## 629 Africa Economy_status_Developing
## 639 Middle East Economy_status_Developing
## 640 Asia Economy_status_Developing
## 651 European Union Economy_status_Developed
## 688 Asia Economy_status_Developing
## 697 Central America and Caribbean Economy_status_Developing
## 700 Africa Economy_status_Developing
## 717 Asia Economy_status_Developing
## 728 Africa Economy_status_Developing
## 733 European Union Economy_status_Developed
## 741 Africa Economy_status_Developing
## 764 Africa Economy_status_Developing
## 766 European Union Economy_status_Developed
## 770 Africa Economy_status_Developing
## 787 Middle East Economy_status_Developing
## 810 Central America and Caribbean Economy_status_Developing
## 811 Central America and Caribbean Economy_status_Developing
## 833 Middle East Economy_status_Developing
## 838 Africa Economy_status_Developing
## 840 Africa Economy_status_Developing
## 850 Asia Economy_status_Developing
## 852 Africa Economy_status_Developing
## 853 Asia Economy_status_Developing
## 869 Asia Economy_status_Developing
## 874 European Union Economy_status_Developed
## 901 Asia Economy_status_Developing
## 903 Africa Economy_status_Developing
## 904 Central America and Caribbean Economy_status_Developing
## 907 Middle East Economy_status_Developing
## 957 Africa Economy_status_Developing
## 1000 Central America and Caribbean Economy_status_Developing
## 1011 Asia Economy_status_Developing
## 1058 Africa Economy_status_Developing
## 1064 European Union Economy_status_Developed
## 1067 Asia Economy_status_Developing
## 1068 Central America and Caribbean Economy_status_Developing
## 1117 Middle East Economy_status_Developing
## 1146 European Union Economy_status_Developed
## 1150 Central America and Caribbean Economy_status_Developing
## 1157 European Union Economy_status_Developed
## 1158 Africa Economy_status_Developing
## 1164 Central America and Caribbean Economy_status_Developing
## 1197 Asia Economy_status_Developed
## 1205 Rest of Europe Economy_status_Developing
## 1206 Africa Economy_status_Developing
## 1225 European Union Economy_status_Developed
## 1227 Africa Economy_status_Developing
## 1251 Central America and Caribbean Economy_status_Developing
## 1262 South America Economy_status_Developing
## 1266 Asia Economy_status_Developing
## 1306 European Union Economy_status_Developed
## 1320 Rest of Europe Economy_status_Developing
## 1338 Africa Economy_status_Developing
## 1358 Africa Economy_status_Developing
## 1481 Africa Economy_status_Developing
## 1492 European Union Economy_status_Developed
## 1503 Africa Economy_status_Developing
## 1531 Rest of Europe Economy_status_Developing
## 1536 European Union Economy_status_Developed
## 1559 South America Economy_status_Developing
## 1566 European Union Economy_status_Developed
## 1588 European Union Economy_status_Developed
## 1604 Asia Economy_status_Developing
## 1614 Rest of Europe Economy_status_Developed
## 1620 Central America and Caribbean Economy_status_Developing
## 1624 Middle East Economy_status_Developing
## 1629 Africa Economy_status_Developing
## 1707 Middle East Economy_status_Developing
## 1710 Africa Economy_status_Developing
## 1713 Asia Economy_status_Developing
## 1716 Rest of Europe Economy_status_Developing
## 1722 South America Economy_status_Developing
## 1732 Oceania Economy_status_Developing
## 1785 Rest of Europe Economy_status_Developing
## 1801 Asia Economy_status_Developing
## 1810 Rest of Europe Economy_status_Developed
## 1820 Africa Economy_status_Developing
## 1824 Rest of Europe Economy_status_Developing
## 1844 Asia Economy_status_Developing
## 1875 Africa Economy_status_Developing
## 1882 Asia Economy_status_Developing
## 1905 South America Economy_status_Developing
## 1948 South America Economy_status_Developing
## 1950 European Union Economy_status_Developed
## 1976 Africa Economy_status_Developing
## 1984 European Union Economy_status_Developed
## 1989 Africa Economy_status_Developing
## 2022 Africa Economy_status_Developing
## 2077 Oceania Economy_status_Developing
## 2081 Asia Economy_status_Developing
## 2118 Middle East Economy_status_Developing
## 2120 European Union Economy_status_Developed
## 2127 European Union Economy_status_Developed
## 2128 Central America and Caribbean Economy_status_Developing
## 2146 South America Economy_status_Developing
## 2148 Oceania Economy_status_Developing
## 2178 Asia Economy_status_Developing
## 2182 European Union Economy_status_Developed
## 2235 Africa Economy_status_Developing
## 2279 Oceania Economy_status_Developed
## 2281 Africa Economy_status_Developing
## 2291 Rest of Europe Economy_status_Developing
## 2322 Central America and Caribbean Economy_status_Developing
## 2324 South America Economy_status_Developing
## 2325 European Union Economy_status_Developed
## 2339 Africa Economy_status_Developing
## 2357 North America Economy_status_Developed
## 2368 South America Economy_status_Developing
## 2379 Asia Economy_status_Developing
## 2396 European Union Economy_status_Developed
## 2405 Africa Economy_status_Developing
## 2410 Asia Economy_status_Developing
## 2443 Rest of Europe Economy_status_Developed
## 2449 Africa Economy_status_Developing
## 2469 European Union Economy_status_Developed
## 2496 Asia Economy_status_Developing
## 2519 European Union Economy_status_Developed
## 2526 Central America and Caribbean Economy_status_Developing
## 2582 Africa Economy_status_Developing
## 2618 Africa Economy_status_Developing
## 2621 South America Economy_status_Developing
## 2642 Oceania Economy_status_Developing
## 2651 Oceania Economy_status_Developing
## 2662 Africa Economy_status_Developing
## 2680 Oceania Economy_status_Developing
## 2702 Asia Economy_status_Developing
## 2711 Africa Economy_status_Developing
## 2713 European Union Economy_status_Developed
## 2728 Asia Economy_status_Developing
## 2738 Oceania Economy_status_Developing
## 2753 Africa Economy_status_Developing
## 2754 Africa Economy_status_Developing
## 2821 South America Economy_status_Developing
## 2841 Africa Economy_status_Developing
## 2847 Central America and Caribbean Economy_status_Developing
## 2849 Middle East Economy_status_Developingdatatwa2=datatwa
datatwa2$mix<-as.factor(paste(datatwa$Region,datatwa$Economy_status))
datatwa2 %>% group_by(mix) %>% summarise(n = n()) ## # A tibble: 14 × 2
## mix n
## <fct> <int>
## 1 Africa Economy_status_Developing 51
## 2 Asia Economy_status_Developed 1
## 3 Asia Economy_status_Developing 26
## 4 Central America and Caribbean Economy_status_Developing 19
## 5 European Union Economy_status_Developed 27
## 6 Middle East Economy_status_Developed 1
## 7 Middle East Economy_status_Developing 13
## 8 North America Economy_status_Developed 2
## 9 North America Economy_status_Developing 1
## 10 Oceania Economy_status_Developed 2
## 11 Oceania Economy_status_Developing 9
## 12 Rest of Europe Economy_status_Developed 4
## 13 Rest of Europe Economy_status_Developing 11
## 14 South America Economy_status_Developing 12datatwa2=datatwa2[!datatwa2["mix"]=="Asia Economy_status_Developed",]
datatwa2=datatwa2[!datatwa2["mix"]=="Middle East Economy_status_Developed",]
datatwa2=datatwa2[!datatwa2["mix"]=="North America Economy_status_Developed",]
datatwa2=datatwa2[!datatwa2["mix"]=="North America Economy_status_Developing",]
datatwa2=datatwa2[!datatwa2["mix"]=="Oceania Economy_status_Developed",]datatwa2 %>% group_by(mix) %>% summarise(n = n()) ## # A tibble: 9 × 2
## mix n
## <fct> <int>
## 1 Africa Economy_status_Developing 51
## 2 Asia Economy_status_Developing 26
## 3 Central America and Caribbean Economy_status_Developing 19
## 4 European Union Economy_status_Developed 27
## 5 Middle East Economy_status_Developing 13
## 6 Oceania Economy_status_Developing 9
## 7 Rest of Europe Economy_status_Developed 4
## 8 Rest of Europe Economy_status_Developing 11
## 9 South America Economy_status_Developing 12datatwa2 %>% group_by(mix) %>% shapiro_test(Thinness_five_nine_years,Thinness_ten_nineteen_years)## # A tibble: 18 × 4
## mix variable statistic p
## <fct> <chr> <dbl> <dbl>
## 1 Africa Economy_status_Developing Thinnes… 0.811 1.33e-6
## 2 Africa Economy_status_Developing Thinnes… 0.839 6.51e-6
## 3 Asia Economy_status_Developing Thinnes… 0.926 6.08e-2
## 4 Asia Economy_status_Developing Thinnes… 0.926 6.23e-2
## 5 Central America and Caribbean Economy_status_Deve… Thinnes… 0.946 3.35e-1
## 6 Central America and Caribbean Economy_status_Deve… Thinnes… 0.940 2.68e-1
## 7 European Union Economy_status_Developed Thinnes… 0.973 6.92e-1
## 8 European Union Economy_status_Developed Thinnes… 0.971 6.30e-1
## 9 Middle East Economy_status_Developing Thinnes… 0.918 2.34e-1
## 10 Middle East Economy_status_Developing Thinnes… 0.924 2.86e-1
## 11 Oceania Economy_status_Developing Thinnes… 0.876 1.43e-1
## 12 Oceania Economy_status_Developing Thinnes… 0.896 2.29e-1
## 13 Rest of Europe Economy_status_Developed Thinnes… 0.935 6.25e-1
## 14 Rest of Europe Economy_status_Developed Thinnes… 0.849 2.23e-1
## 15 Rest of Europe Economy_status_Developing Thinnes… 0.920 3.16e-1
## 16 Rest of Europe Economy_status_Developing Thinnes… 0.884 1.16e-1
## 17 South America Economy_status_Developing Thinnes… 0.906 1.88e-1
## 18 South America Economy_status_Developing Thinnes… 0.927 3.47e-1boxM(Y = cbind(datatwa$Thinness_five_nine_years,datatwa$Thinness_ten_nineteen_years), group = factor(datatwa$Region))##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: cbind(datatwa$Thinness_five_nine_years, datatwa$Thinness_ten_nineteen_years)
## Chi-Sq (approx.) = 453.64, df = 24, p-value < 2.2e-16m2 <- manova(cbind(Thinness_five_nine_years,Thinness_ten_nineteen_years) ~ Region*Economy_status, data = datatwa)
summary(m2)## Df Pillai approx F num Df den Df Pr(>F)
## Region 8 0.69743 11.0431 16 330 < 2.2e-16 ***
## Economy_status 1 0.10480 9.6001 2 164 0.0001141 ***
## Region:Economy_status 4 0.02408 0.5026 8 330 0.8541490
## Residuals 165
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary.aov(m2)## Response Thinness_five_nine_years :
## Df Sum Sq Mean Sq F value Pr(>F)
## Region 8 175.961 21.9951 34.3828 < 2.2e-16 ***
## Economy_status 1 12.085 12.0851 18.8915 2.412e-05 ***
## Region:Economy_status 4 1.634 0.4084 0.6384 0.6358
## Residuals 165 105.552 0.6397
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Response Thinness_ten_nineteen_years :
## Df Sum Sq Mean Sq F value Pr(>F)
## Region 8 172.664 21.5830 37.5591 < 2.2e-16 ***
## Economy_status 1 8.202 8.2017 14.2727 0.0002205 ***
## Region:Economy_status 4 2.091 0.5228 0.9097 0.4597268
## Residuals 165 94.816 0.5746
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Fisher Discriminant Analysis (Linear Discriminant Analysis
library(MASS)
library(klaR)
library(ggplot2)
library(GGally)
library(mlbench)
library(ggord)data_lda=subset(data,select = -c(Country,Region))
str(data_lda)## 'data.frame': 179 obs. of 17 variables:
## $ Infant_deaths : num 11.1 2.7 6.6 57 39.7 21.6 9.6 41.3 2.2 17.4 ...
## $ Under_five_deaths : num 13 3.3 8.2 88 59.8 25.2 11.2 59 2.7 21.8 ...
## $ Adult_mortality : num 105.8 57.9 223 340.1 261.7 ...
## $ Alcohol_consumption : num 1.32 10.35 8.06 4.55 2.69 ...
## $ Hepatitis_B : num 97 97 97 84 97 95 99 69 88 97 ...
## $ Measles : num 65 94 97 64 64 99 98 64 91 65 ...
## $ BMI : num 27.8 26 26.2 24.3 23.9 25.5 26.3 21.3 26.6 21.7 ...
## $ Polio : num 97 97 97 77 96 95 99 68 95 97 ...
## $ Diphtheria : num 97 97 97 84 97 95 99 69 95 97 ...
## $ Incidents_HIV : num 0.08 0.09 0.08 1.12 0.96 0.05 0.05 0.24 0.04 0.12 ...
## $ GDP_per_capita : num 11006 25742 9313 1383 661 ...
## $ Population_mln : num 78.53 46.44 144.1 23.3 2.09 ...
## $ Thinness_ten_nineteen_years: num 4.9 0.6 2.3 5.6 7.3 6 7.1 7.1 0.8 14.2 ...
## $ Thinness_five_nine_years : num 4.8 0.5 2.3 5.5 7.2 5.8 6.9 7.1 0.7 14.5 ...
## $ Schooling : num 7.8 9.7 12 6.1 3.4 7.9 9.5 6.1 12.5 8 ...
## $ Life_expectancy : num 76.5 82.8 71.2 57.6 60.9 76.1 76.9 65.5 82.3 75.1 ...
## $ Economy_status : Factor w/ 2 levels "Economy_status_Developed",..: 2 1 2 2 2 2 2 2 1 2 ...#make this example reproducible
set.seed(467)
#Use 80% of dataset as training set and remaining 20% as testing set
sample <- sample(c(TRUE, FALSE), nrow(data), replace=TRUE, prob=c(0.8,0.2))
train <- data_lda[sample, ]
test <- data_lda[!sample, ] model <- lda(Economy_status~.,data = train)
model## Call:
## lda(Economy_status ~ ., data = train)
##
## Prior probabilities of groups:
## Economy_status_Developed Economy_status_Developing
## 0.2255639 0.7744361
##
## Group means:
## Infant_deaths Under_five_deaths Adult_mortality
## Economy_status_Developed 3.573333 4.29000 79.24293
## Economy_status_Developing 29.301942 39.26796 189.34433
## Alcohol_consumption Hepatitis_B Measles BMI
## Economy_status_Developed 9.727333 91.30000 89.93333 26.44333
## Economy_status_Developing 3.353592 86.12621 76.49515 25.20777
## Polio Diphtheria Incidents_HIV GDP_per_capita
## Economy_status_Developed 94.86667 95.23333 0.0750000 36783.267
## Economy_status_Developing 86.25243 85.72816 0.8687379 6456.495
## Population_mln Thinness_ten_nineteen_years
## Economy_status_Developed 32.17500 1.233333
## Economy_status_Developing 50.33204 5.362136
## Thinness_five_nine_years Schooling Life_expectancy
## Economy_status_Developed 1.173333 12.146667 80.21667
## Economy_status_Developing 5.476699 7.256311 68.95728
##
## Coefficients of linear discriminants:
## LD1
## Infant_deaths 2.035438e-02
## Under_five_deaths -5.244384e-02
## Adult_mortality 2.219491e-03
## Alcohol_consumption -2.546864e-01
## Hepatitis_B 5.255349e-02
## Measles 1.317721e-02
## BMI 4.961314e-02
## Polio -2.223254e-03
## Diphtheria -4.900140e-02
## Incidents_HIV -8.602644e-03
## GDP_per_capita -2.145562e-05
## Population_mln 2.557071e-04
## Thinness_ten_nineteen_years 1.158591e-02
## Thinness_five_nine_years 1.781007e-02
## Schooling -1.635261e-01
## Life_expectancy -1.411105e-01plot(model)
model.values <- predict(model)
names(model.values)## [1] "class" "posterior" "x"partimat(as.factor(Economy_status)~.,data=train,method="lda") 
train_predict<- predict(model,train)$class
table_train <- table(Predicted =train_predict, Actual = train$Economy_status)
table_train## Actual
## Predicted Economy_status_Developed Economy_status_Developing
## Economy_status_Developed 28 2
## Economy_status_Developing 2 101sum(diag(table_train))/sum(table_train)## [1] 0.9699248test_predict<- predict(model,test)$class
table_test<- table(Predicted =test_predict, Actual = test$Economy_status)
table_test## Actual
## Predicted Economy_status_Developed Economy_status_Developing
## Economy_status_Developed 7 1
## Economy_status_Developing 0 38sum(diag(table_test))/sum(table_test)## [1] 0.9782609Cluster Analysis
datacl=data[, c("Infant_deaths", "Under_five_deaths", "Adult_mortality", "Thinness_ten_nineteen_years","Thinness_five_nine_years","Life_expectancy","Region")]X <- scale(datacl[, c("Infant_deaths", "Under_five_deaths", "Adult_mortality", "Thinness_ten_nineteen_years","Thinness_five_nine_years","Life_expectancy")], center = FALSE, scale = TRUE)
dj <- dist(X)
plot(cc <- hclust(dj), main = "Jets clustering")
cc##
## Call:
## hclust(d = dj)
##
## Cluster method : complete
## Distance : euclidean
## Number of objects: 179Divisive Hierarchical Clustering
library(cluster)
library(factoextra)## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBares.diana <- diana(datacl[, c("Infant_deaths", "Under_five_deaths", "Adult_mortality", "Thinness_ten_nineteen_years","Thinness_five_nine_years","Life_expectancy")], stand = TRUE)
# Plot the dendrogram
fviz_dend(res.diana, cex = 0.5,
k = 6, # Cut in four groups
palette = "jco" # Color palette
)
K-means Clustering
datacl2=data[, c('Hepatitis_B',
'Measles',
'Polio','Diphtheria',
'Incidents_HIV')]scatterplotMatrix(datacl2)
library("lattice")datacl_dist <- dist(datacl_1 <- scale(datacl2, center = FALSE))
levelplot(as.matrix(datacl_dist), xlab = "States", ylab = "States")
sapply(datacl2, var)## Hepatitis_B Measles Polio Diphtheria Incidents_HIV
## 200.720168 261.986567 169.632917 215.908669 2.628673rge <- sapply(datacl2, function(x) diff(range(x)))
datacl_s <- sweep(datacl2, 2, rge, FUN = "/")
sapply(datacl_s, var)## Hepatitis_B Measles Polio Diphtheria Incidents_HIV
## 0.03385397 0.04306157 0.04412927 0.03134108 0.01287277n <- nrow(datacl_s)
wss <- rep(0, 6)
wss[1] <- (n - 1) * sum(sapply(datacl_s, var))
for (i in 2:6)
wss[i] <- sum(kmeans(datacl_s,centers = i)$withinss)
plot(1:6, wss, type = "b", xlab = "Number of groups", ylab = "Within groups sum of squares")
kmeans(datacl_s, centers = 2)$centers * rge## Hepatitis_B Measles Polio Diphtheria Incidents_HIV
## 1 92.98551 67.87514 21.67550 88.63017 3.2454691
## 2 68.16661 66.88274 85.45122 49.59271 0.7814634kmeans(datacl_s, centers = 2)$cluster## 1 2 7 28 44 58 75 102 111 113 122 161 167 174 183 203
## 2 2 2 1 2 2 2 1 2 2 2 2 2 2 1 2
## 217 220 242 269 272 301 304 331 334 416 427 444 452 474 488 496
## 1 1 2 2 2 1 2 1 2 2 1 2 1 2 2 2
## 499 512 547 557 559 580 585 591 599 609 627 629 639 640 651 688
## 1 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2
## 697 700 717 728 733 741 764 766 770 787 810 811 833 838 840 850
## 2 2 2 2 2 2 2 2 2 1 2 1 2 2 1 2
## 852 853 869 874 901 903 904 907 957 1000 1011 1058 1064 1067 1068 1117
## 1 2 2 2 2 2 2 2 1 2 1 2 2 1 2 1
## 1146 1150 1157 1158 1164 1197 1205 1206 1225 1227 1251 1262 1266 1306 1320 1338
## 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 1
## 1358 1481 1492 1503 1531 1536 1559 1566 1588 1604 1614 1620 1624 1629 1707 1710
## 2 2 2 1 2 2 2 2 2 2 2 1 2 1 1 2
## 1713 1716 1722 1732 1785 1801 1810 1820 1824 1844 1875 1882 1905 1948 1950 1976
## 2 2 2 1 2 2 2 1 2 2 1 2 2 2 2 1
## 1984 1989 2022 2077 2081 2118 2120 2127 2128 2146 2148 2178 2182 2235 2279 2281
## 2 2 2 1 2 2 2 2 2 2 1 2 2 1 2 2
## 2291 2322 2324 2325 2339 2357 2368 2379 2396 2405 2410 2443 2449 2469 2496 2519
## 2 2 1 2 2 2 2 2 2 2 2 2 2 2 1 2
## 2526 2582 2618 2621 2642 2651 2662 2680 2702 2711 2713 2728 2738 2753 2754 2821
## 1 1 2 2 1 2 1 1 2 1 2 2 2 1 2 2
## 2841 2847 2849
## 2 2 2Principal Component Analysis
data_numeric<- data[, c('Infant_deaths',
'BMI',
'GDP_per_capita',
'Schooling',
'Life_expectancy',
'Under_five_deaths',
'Alcohol_consumption',
'Hepatitis_B',
'Measles',
'Polio','Diphtheria',
'Incidents_HIV',
'Population_mln',
'Thinness_ten_nineteen_years',
'Thinness_five_nine_years')]data_dis<- data[, c(
'Life_expectancy','Under_five_deaths',
'Alcohol_consumption','Infant_deaths',
'Hepatitis_B','Measles','Alcohol_consumption',
'Polio','Diphtheria','Incidents_HIV',
'Thinness_ten_nineteen_years',
'Thinness_five_nine_years')]scatterplotMatrix(data_dis, diagonal="histogram")
res <- cor(data_dis, method="pearson")
corrplot::corrplot(res, method= "color", order = "hclust")
data_dis<-scale(data_dis)
data_dis## Life_expectancy Under_five_deaths Alcohol_consumption Infant_deaths
## 1 0.643020804 -0.579830261 -0.910686853 -0.579809404
## 2 1.447385265 -0.880912648 1.501608764 -0.970734215
## 7 -0.033666758 -0.728819483 0.889852733 -0.789233410
## 28 -1.770072577 1.748126333 -0.047816992 1.556315454
## 44 -1.348738812 0.872814653 -0.544701804 0.751196499
## 58 0.591950045 -0.201149322 -1.116386479 -0.091153391
## 75 0.694091564 -0.635701220 -1.143100717 -0.649617406
## 102 -0.761425079 0.847983116 -1.033572344 0.825658367
## 111 1.383546816 -0.899536300 0.331525176 -0.994003549
## 113 0.464273147 -0.306683354 -0.467230516 -0.286615796
## 122 -2.050961754 0.792112158 0.737581581 1.007159172
## 161 -0.531606662 0.559316499 0.376939379 0.746542632
## 167 0.387667007 -0.828145632 1.621822832 -0.896272346
## 174 -0.250717485 0.118556717 -1.199200615 0.262540485
## 183 -1.553021850 1.993337761 -0.069188382 2.300934141
## 203 0.272757799 -0.856081111 1.352009036 -0.952118748
## 217 -1.540254160 1.751230275 0.481124904 1.588892522
## 220 -0.033666758 -0.688468236 0.350225142 -0.719425408
## 242 1.038819190 -0.700884004 -0.411130618 -0.738040875
## 269 1.358011436 -0.862288995 -0.531344685 -0.947464881
## 272 1.281405297 -0.812625921 1.055481004 -0.882310746
## 301 -2.344618621 3.011430778 -1.087000819 2.426588544
## 304 0.094010141 -0.278747875 -0.993500988 -0.198192327
## 331 -0.199646726 -0.061471926 -1.220572004 0.057770346
## 334 -1.846678716 1.875387960 -0.427159160 1.695931458
## 416 0.387667007 -0.387385850 -0.598130278 -0.328500597
## 427 -1.514718780 2.347187163 -1.161800683 2.086856268
## 444 1.370779126 -0.893328416 0.641410327 -0.989349682
## 452 -0.084737517 -0.123550769 -1.241943394 -0.016691522
## 474 0.221687039 0.103037006 0.176582600 0.243925018
## 488 0.438737767 -0.480504113 -0.130631127 -0.449501134
## 496 0.911142291 -0.884016590 2.145421881 -0.980041949
## 499 -1.387041882 2.046104777 -0.854586955 1.844855195
## 512 0.081242451 -0.464984403 0.716210191 -0.389000866
## 547 -0.531606662 0.804527927 -1.169814954 0.983889838
## 557 0.451505457 -0.489815940 0.507839141 -0.435539534
## 559 -0.276252865 0.044062106 0.200625414 0.178770883
## 580 0.566414665 -0.651220930 0.248711041 -0.710117674
## 585 -0.863566598 0.453782466 -0.988158141 0.485926091
## 591 0.464273147 -0.710195831 -1.263314784 -0.747348609
## 599 1.332476056 -0.815729863 0.873824191 -0.877656879
## 609 0.119545521 -0.480504113 0.927252665 -0.430885667
## 627 0.834536152 -0.685364294 -0.106588314 -0.700809941
## 629 -2.612740107 1.952986513 -0.443187702 2.282318674
## 639 0.413202387 -0.700884004 -1.263314784 -0.733387008
## 640 -0.365626694 0.366872087 -0.461887668 0.527810893
## 651 0.362131628 -0.831249574 2.530106896 -0.910233947
## 688 -0.480535902 0.326520839 -0.365716415 0.597618895
## 697 0.643020804 -0.741235252 1.156995105 -0.793887277
## 700 -1.208294224 0.671058415 -0.718344345 0.611580495
## 717 -0.723122010 0.636915052 -0.870615497 0.811696767
## 728 0.362131628 -0.523959303 1.060823851 -0.505347536
## 733 1.281405297 -0.859185053 0.953966902 -0.938157147
## 741 -1.450880331 1.114922139 -0.197416720 1.053697840
## 764 -1.821143337 1.623968648 -0.937401090 1.756431726
## 766 0.400434697 -0.728819483 1.645865645 -0.775271810
## 770 -2.370154000 3.368384122 -0.445859126 3.329438702
## 787 -0.199646726 0.307897187 -1.201872038 0.095001281
## 810 0.119545521 -0.502231708 -0.584773160 -0.477424335
## 811 0.809000773 -0.455672576 0.563939039 -0.416924066
## 833 0.336596248 -0.440152866 -1.183172072 -0.398308599
## 838 -1.067849635 0.820047637 0.836424259 0.807042900
## 840 -0.838031218 0.577940151 0.889852733 0.583657294
## 850 0.106777831 -0.167005959 -1.127072174 -0.012037655
## 852 -2.344618621 2.940040109 -0.058502687 2.594127749
## 853 0.591950045 -0.648116988 0.593324700 -0.663579007
## 869 -0.301788244 -0.381177965 0.967324021 -0.323846731
## 874 1.230334538 -0.871600821 1.498937341 -0.956772615
## 901 0.796233083 -0.679156409 -0.926715395 -0.705463808
## 903 -1.016778876 1.260807419 -1.225914852 1.435314917
## 904 0.183383970 -0.384281908 0.331525176 -0.291269663
## 907 0.745162323 -0.747443136 -0.696972956 -0.793887277
## 957 -1.284900363 0.745553026 0.724224462 0.713965564
## 1000 -0.263485175 -0.266332107 0.072397075 -0.235423262
## 1011 -0.620980491 1.375653278 -1.252629089 1.793662660
## 1058 -1.106152705 0.711409663 -0.795815633 0.709311698
## 1064 1.281405297 -0.905744185 1.012738224 -1.003311282
## 1067 -1.029546566 1.201832519 -1.263314784 1.379468516
## 1068 0.323828558 -0.508439593 0.529210531 -0.482078202
## 1117 0.936677671 -0.725715541 -0.956101056 -0.765964076
## 1146 1.192031468 -0.902640243 1.806151068 -0.998657416
## 1150 0.336596248 -0.502231708 -0.389759228 -0.472770468
## 1157 1.217566848 -0.856081111 1.504280188 -0.942811014
## 1158 -1.795607957 1.909531323 0.903209852 2.049625334
## 1164 0.936677671 -0.548790840 1.322623375 -0.491385935
## 1197 1.575062164 -0.899536300 1.020752495 -1.003311282
## 1205 0.502576216 -0.629493335 -0.309616517 -0.631001939
## 1206 0.540879286 -0.253916338 -1.159129259 -0.156307526
## 1225 0.655788494 -0.790898326 1.480237375 -0.859041412
## 1227 -0.608212801 0.550004672 -1.212557733 0.518503159
## 1251 0.528111596 -0.303579412 1.202409308 -0.188884594
## 1262 0.643020804 -0.502231708 -0.152002517 -0.472770468
## 1266 -0.174111346 0.180635559 -1.017543802 0.420771956
## 1306 1.243102227 -0.868496879 1.835536729 -0.956772615
## 1320 0.004636312 -0.492919882 0.542567650 -0.463462734
## 1338 -1.067849635 0.649330820 -0.715672922 0.653465296
## 1358 -1.195526534 0.494133714 -0.560730346 0.453349024
## 1481 -1.527486470 0.919373785 -0.237488076 0.862889302
## 1492 1.332476056 -0.778482557 0.705524496 -0.831118211
## 1503 -0.850798908 0.534484962 -0.822529870 0.541772493
## 1531 0.630253115 -0.859185053 1.004723953 -0.942811014
## 1536 1.217566848 -0.846769284 0.521196260 -0.919541680
## 1559 -0.148575966 -0.011808852 -0.421816313 0.085693547
## 1566 1.281405297 -0.868496879 1.624494256 -0.947464881
## 1588 0.745162323 -0.831249574 1.311937680 -0.900926213
## 1604 -0.097505207 -0.291163644 0.171239753 -0.170269126
## 1614 1.460152955 -0.849873226 1.306594833 -0.924195547
## 1620 0.234454729 -0.104927116 -0.822529870 0.006577812
## 1624 1.064354570 -0.741235252 -0.988158141 -0.784579543
## 1629 -0.965708117 1.583617400 -1.263314784 1.463238118
## 1707 -0.684818940 0.900750133 -1.255300513 1.049043973
## 1710 -1.246597293 1.118026081 -0.328316483 1.086274908
## 1713 0.068474761 -0.613973625 -0.373730686 -0.603078738
## 1716 0.489808526 -0.787794384 0.660110293 -0.845079811
## 1722 0.285525489 -0.291163644 0.128496973 -0.212153928
## 1732 -0.531606662 -0.086303463 -0.838558413 0.029847146
## 1785 0.694091564 -0.787794384 0.045682838 -0.845079811
## 1801 0.489808526 -0.654324872 -1.084329395 -0.686848341
## 1810 1.217566848 -0.843665342 1.298580562 -0.919541680
## 1820 -1.387041882 1.928154976 -1.231257699 1.314314381
## 1824 0.387667007 -0.545686898 -0.184059602 -0.510001402
## 1844 0.004636312 0.199259212 -1.260643360 0.346310088
## 1875 -1.987123305 3.185251537 -1.263314784 2.794244021
## 1882 -0.071969827 -0.384281908 -0.571416041 -0.291269663
## 1905 0.757930013 -0.707091889 0.339539447 -0.742694742
## 1948 1.038819190 -0.738131310 0.844438530 -0.784579543
## 1950 1.166496088 -0.862288995 1.691279848 -0.942811014
## 1976 -1.169991154 1.757438159 -0.413802042 1.900701597
## 1984 1.179263778 -0.856081111 1.253166359 -0.933503281
## 1989 -0.506071282 0.497237656 0.422353582 0.513849292
## 2022 0.374899318 -0.533271130 -0.507301872 -0.500693669
## 2077 -1.016778876 0.599667746 -0.900001158 0.774465833
## 2081 1.434617575 -0.899536300 -0.777115667 -0.994003549
## 2118 0.553646976 -0.502231708 -1.260643360 -0.477424335
## 2120 0.770697703 -0.831249574 1.533665849 -0.900926213
## 2127 1.409082196 -0.874704763 0.644081751 -0.956772615
## 2128 0.911142291 -0.806418037 -0.021102755 -0.886964613
## 2146 0.553646976 -0.496023824 0.254053888 -0.528616870
## 2148 -0.199646726 -0.108031058 -0.883972616 0.001923945
## 2178 -0.365626694 0.003710858 -0.371059262 0.174117016
## 2182 0.528111596 -0.825041689 1.661894188 -0.900926213
## 2235 -2.625507797 2.843817903 -1.022886649 2.994360293
## 2279 1.396314506 -0.862288995 1.322623375 -0.942811014
## 2281 -0.020899068 -0.260124222 -1.215229157 -0.174922993
## 2291 0.196151660 -0.657428815 0.593324700 -0.658925140
## 2322 0.208919350 -0.548790840 1.213095003 -0.537924603
## 2324 -0.033666758 -0.353242486 0.005611482 -0.249384862
## 2325 1.383546816 -0.896432358 1.774093984 -0.989349682
## 2339 0.081242451 -0.570518435 -1.260643360 -0.565847804
## 2357 0.923909981 -0.772274673 1.082195241 -0.826464344
## 2368 0.591950045 -0.626389393 1.004723953 -0.621694205
## 2379 -0.135808276 0.044062106 -1.252629089 0.178770883
## 2396 1.140960709 -0.893328416 1.298580562 -0.984695815
## 2405 0.081242451 -0.378074023 -0.050488416 -0.319192864
## 2410 -0.633748181 0.686578126 0.630724632 0.862889302
## 2443 1.409082196 -0.911952069 0.782995784 -1.012619016
## 2449 -1.476415711 1.372549336 -0.900001158 1.267775713
## 2469 0.783465393 -0.887120532 3.203305673 -0.984695815
## 2496 -0.110272897 -0.064575869 -0.055831263 -0.007383789
## 2519 0.438737767 -0.697780062 1.261180630 -0.738040875
## 2526 -1.144455775 1.186312808 -0.520658990 1.360853049
## 2582 -1.961587925 1.835036712 -0.851915531 1.961201865
## 2618 -1.476415711 2.148534867 0.614696090 1.677315991
## 2621 0.591950045 -0.505335650 -0.277559432 -0.482078202
## 2642 -0.378394384 0.574836209 -1.153786412 0.895466369
## 2651 -0.557142041 -0.225980859 -0.560730346 -0.137692059
## 2662 -1.782840267 2.378226584 -1.097686513 2.012394400
## 2680 0.157848590 -0.406009502 -0.702315803 -0.356423798
## 2702 0.617485425 -0.713299773 -0.536687533 -0.747348609
## 2711 -0.825263528 0.953517149 -1.060286581 0.914081836
## 2713 1.383546816 -0.852977169 1.907665170 -0.947464881
## 2728 0.515343906 -0.731923426 -1.116386479 -0.775271810
## 2738 -0.123040587 -0.598453914 -1.201872038 -0.598424871
## 2753 -1.131688085 0.143388254 0.660110293 0.234617285
## 2754 0.566414665 -0.449464692 -0.862601226 -0.407616333
## 2821 0.145080900 -0.390489792 0.395639345 -0.333154464
## 2841 -0.940172737 1.059051181 -1.177829225 1.444622651
## 2847 0.272757799 -0.381177965 -0.269545161 -0.323846731
## 2849 0.681323874 -0.747443136 -0.854586955 -0.793887277
## Hepatitis_B Measles Alcohol_consumption.1 Polio Diphtheria
## 1 0.698739316 -0.94087799 -0.910686853 0.67085499 0.618204939
## 2 0.698739316 0.85079393 1.501608764 0.67085499 0.618204939
## 7 0.698739316 1.03613930 0.889852733 0.67085499 0.618204939
## 28 -0.218848939 -1.00265978 -0.047816992 -0.86473379 -0.266520088
## 44 0.698739316 -1.00265978 -0.544701804 0.59407555 0.618204939
## 58 0.557571892 1.15970288 -1.116386479 0.51729611 0.482093397
## 75 0.839906740 1.09792109 -1.143100717 0.82441387 0.754316482
## 102 -1.277604618 -1.00265978 -1.033572344 -1.55574875 -1.287356657
## 111 0.063485909 0.66544856 0.331525176 0.51729611 0.482093397
## 113 0.698739316 -0.94087799 -0.467230516 0.67085499 0.618204939
## 122 0.204653332 0.17119423 0.737581581 -0.32727772 0.141814540
## 161 0.557571892 -0.01415114 0.376939379 0.59407555 0.482093397
## 167 0.486988180 0.72723035 1.621822832 0.44051667 0.482093397
## 174 0.275237044 -0.94087799 -1.199200615 0.13339891 0.209870311
## 183 -0.430600075 -1.00265978 -0.069188382 -0.78795436 -0.470687401
## 203 0.839906740 1.15970288 1.352009036 0.82441387 0.754316482
## 217 -1.630523178 -1.00265978 0.481124904 -2.01642538 -1.627635513
## 220 -4.595039080 -1.43513231 0.350225142 -2.86099921 -4.417922136
## 242 0.345820756 0.60366677 -0.411130618 0.28695779 0.277926083
## 269 0.628155604 1.03613930 -0.531344685 0.51729611 0.482093397
## 272 0.345820756 0.41832139 1.055481004 0.28695779 0.277926083
## 301 -2.901029993 -1.00265978 -1.087000819 -2.78421977 -2.852639397
## 304 0.769323028 -0.94087799 -0.993500988 -0.25049828 0.686260710
## 331 -2.195192874 -0.26127830 -1.220572004 -1.24863099 -2.035970141
## 334 -0.007097803 -1.00265978 -0.427159160 -0.40405716 -0.062352774
## 416 0.698739316 0.17119423 -0.598130278 0.74763443 0.618204939
## 427 -2.336360298 -1.00265978 -1.161800683 -3.16811697 -2.308193226
## 444 -1.418772042 0.91257572 0.641410327 0.74763443 0.686260710
## 452 -0.642351211 -3.04145885 -1.241943394 -0.25049828 -0.674854715
## 474 -0.430600075 0.17119423 0.176582600 -0.09693940 -0.198464316
## 488 -0.360016363 0.97435751 -0.130631127 -0.09693940 -0.062352774
## 496 0.698739316 1.15970288 2.145421881 0.67085499 0.618204939
## 499 -0.360016363 0.17119423 -0.854586955 -1.24863099 -0.402631630
## 512 0.769323028 0.17119423 0.716210191 0.67085499 0.686260710
## 547 -0.360016363 -0.26127830 -1.169814954 -0.63439548 -0.674854715
## 557 0.628155604 -0.01415114 0.507839141 0.74763443 0.550149168
## 559 0.557571892 0.91257572 0.200625414 0.28695779 0.482093397
## 580 0.839906740 1.15970288 0.248711041 0.82441387 0.754316482
## 585 0.557571892 0.48010318 -0.988158141 0.51729611 0.482093397
## 591 0.839906740 0.97435751 -1.263314784 0.82441387 0.754316482
## 599 -2.265776586 0.35653960 0.873824191 0.21017835 0.209870311
## 609 0.345820756 0.54188497 0.927252665 0.82441387 0.277926083
## 627 0.839906740 1.09792109 -0.106588314 0.82441387 0.754316482
## 629 0.416404468 0.10941244 -0.443187702 -0.25049828 0.345981854
## 639 0.769323028 0.97435751 -1.263314784 0.67085499 0.686260710
## 640 -0.007097803 -0.69375083 -0.461887668 -0.17371884 -0.062352774
## 651 0.486988180 0.72723035 2.530106896 0.36373723 0.345981854
## 688 0.839906740 1.15970288 -0.365716415 0.82441387 0.754316482
## 697 0.839906740 0.23297602 1.156995105 -0.17371884 0.754316482
## 700 0.063485909 -1.00265978 -0.718344345 -0.02015996 0.005702998
## 717 0.134069620 -0.13771472 -0.870615497 0.05661947 0.073758769
## 728 0.769323028 1.09792109 1.060823851 0.67085499 0.618204939
## 733 0.486988180 0.72723035 0.953966902 0.51729611 0.482093397
## 741 0.486988180 -0.94087799 -0.197416720 0.44051667 0.414037625
## 764 0.063485909 -1.00265978 -0.937401090 -0.02015996 -0.538743173
## 766 0.345820756 0.41832139 1.645865645 0.21017835 0.209870311
## 770 -0.077681515 -1.24978694 -0.445859126 -0.17371884 -0.130408545
## 787 -3.253948553 -2.05295021 -1.201872038 -2.93777865 -3.192918253
## 810 0.275237044 0.48010318 -0.584773160 0.28695779 0.209870311
## 811 -0.995269771 0.72723035 0.563939039 -1.24863099 -1.015133572
## 833 0.839906740 0.97435751 -1.183172072 0.82441387 0.754316482
## 838 0.769323028 -1.00265978 0.836424259 0.59407555 0.686260710
## 840 -0.501183787 -1.00265978 0.889852733 -0.71117492 -0.538743173
## 850 0.628155604 1.09792109 -1.127072174 0.74763443 0.550149168
## 852 -2.689278857 -1.00265978 -0.058502687 -3.55201416 -2.648472083
## 853 0.839906740 0.91257572 0.593324700 0.82441387 0.754316482
## 869 0.839906740 1.09792109 0.967324021 0.82441387 0.754316482
## 874 0.769323028 0.91257572 1.498937341 0.74763443 0.686260710
## 901 0.839906740 1.15970288 -0.926715395 0.82441387 0.754316482
## 903 0.275237044 -1.00265978 -1.225914852 0.28695779 0.209870311
## 904 0.204653332 -0.07593293 0.331525176 -0.02015996 0.550149168
## 907 0.839906740 1.15970288 -0.696972956 0.82441387 0.754316482
## 957 -0.642351211 -1.00265978 0.724224462 -0.25049828 -0.674854715
## 1000 0.628155604 -0.26127830 0.072397075 0.59407555 0.550149168
## 1011 -1.065853483 -1.62047768 -1.252629089 -1.24863099 -1.083189343
## 1058 0.063485909 -1.06444157 -0.795815633 -0.02015996 0.005702998
## 1064 0.063485909 0.72723035 1.012738224 0.67085499 0.618204939
## 1067 -1.559939466 -2.36185916 -1.263314784 -1.63252818 -1.559579742
## 1068 0.486988180 0.91257572 0.529210531 0.44051667 0.414037625
## 1117 -0.430600075 -1.06444157 -0.956101056 -0.55761604 -0.470687401
## 1146 0.063485909 0.97435751 1.806151068 0.51729611 0.482093397
## 1150 0.275237044 0.17119423 -0.389759228 0.21017835 0.209870311
## 1157 0.769323028 0.29475781 1.504280188 0.82441387 0.754316482
## 1158 -3.324532265 -1.00265978 0.903209852 -3.93591136 -4.894312535
## 1164 0.698739316 0.54188497 1.322623375 0.67085499 0.618204939
## 1197 -0.289432651 0.78901214 1.020752495 0.82441387 0.550149168
## 1205 0.345820756 1.03613930 -0.309616517 0.28695779 0.209870311
## 1206 0.839906740 0.91257572 -1.159129259 0.82441387 0.754316482
## 1225 0.628155604 1.03613930 1.480237375 0.59407555 0.550149168
## 1227 0.134069620 -1.62047768 -1.212557733 -0.25049828 0.073758769
## 1251 0.839906740 0.17119423 1.202409308 0.82441387 0.754316482
## 1262 0.275237044 0.35653960 -0.152002517 0.21017835 0.209870311
## 1266 0.628155604 0.85079393 -1.017543802 0.59407555 0.550149168
## 1306 0.416404468 0.48010318 1.835536729 0.36373723 0.345981854
## 1320 0.063485909 0.72723035 0.542567650 -0.02015996 -0.062352774
## 1338 -0.501183787 -1.00265978 -0.715672922 -0.63439548 -0.538743173
## 1358 0.345820756 -1.00265978 -0.560730346 0.28695779 0.277926083
## 1481 -0.007097803 -1.00265978 -0.237488076 -0.02015996 -0.062352774
## 1492 0.557571892 0.66544856 0.705524496 0.67085499 0.618204939
## 1503 0.134069620 -3.22680422 -0.822529870 -0.40405716 0.073758769
## 1531 -0.360016363 0.85079393 1.004723953 0.05661947 0.073758769
## 1536 0.628155604 0.17119423 0.521196260 0.82441387 0.754316482
## 1559 0.839906740 0.17119423 -0.421816313 0.82441387 0.754316482
## 1566 0.557571892 0.35653960 1.624494256 0.51729611 0.482093397
## 1588 0.486988180 0.97435751 1.311937680 0.44051667 0.414037625
## 1604 0.698739316 -0.94087799 0.171239753 0.67085499 0.618204939
## 1614 0.063485909 0.41832139 1.306594833 0.59407555 0.618204939
## 1620 -0.924686059 0.17119423 -0.822529870 -1.47896931 -0.947077800
## 1624 0.839906740 0.66544856 -0.988158141 0.82441387 0.754316482
## 1629 -0.995269771 -1.00265978 -1.263314784 -1.63252818 -1.015133572
## 1707 -1.277604618 0.91257572 -1.255300513 -1.93964594 -1.287356657
## 1710 0.204653332 -2.05295021 -0.328316483 0.13339891 0.141814540
## 1713 0.769323028 1.09792109 -0.373730686 0.74763443 0.686260710
## 1716 0.486988180 0.35653960 0.660110293 0.51729611 0.482093397
## 1722 0.416404468 -0.50840546 0.128496973 0.36373723 0.345981854
## 1732 -0.642351211 -0.94087799 -0.838558413 -1.32541043 -1.083189343
## 1785 -0.360016363 0.48010318 0.045682838 -1.09507211 -0.402631630
## 1801 0.839906740 1.03613930 -1.084329395 0.82441387 0.754316482
## 1810 0.063485909 0.35653960 1.298580562 0.59407555 0.550149168
## 1820 -1.559939466 -1.00265978 -1.231257699 -0.40405716 -1.559579742
## 1824 0.486988180 1.03613930 -0.184059602 0.59407555 0.414037625
## 1844 0.698739316 0.60366677 -1.260643360 0.74763443 0.618204939
## 1875 -3.183364841 -1.00265978 -1.263314784 -3.16811697 -3.124862482
## 1882 0.839906740 1.15970288 -0.571416041 0.82441387 0.754316482
## 1905 0.557571892 0.78901214 0.339539447 0.51729611 0.482093397
## 1948 0.698739316 0.54188497 0.844438530 0.59407555 0.550149168
## 1950 0.063485909 0.78901214 1.691279848 0.28695779 0.482093397
## 1976 -2.477527722 -1.00265978 -0.413802042 -1.78608706 -2.444304769
## 1984 0.063485909 -0.01415114 1.253166359 0.36373723 0.345981854
## 1989 0.769323028 0.41832139 0.422353582 0.82441387 0.686260710
## 2022 0.698739316 0.97435751 -0.507301872 0.74763443 0.618204939
## 2077 -1.418772042 -0.94087799 -0.900001158 -2.86099921 -1.015133572
## 2081 0.628155604 0.60366677 -0.777115667 0.59407555 0.550149168
## 2118 0.769323028 -0.94087799 -1.260643360 0.74763443 0.686260710
## 2120 0.628155604 0.85079393 1.533665849 0.28695779 0.686260710
## 2127 0.416404468 0.17119423 0.644081751 0.36373723 0.345981854
## 2128 0.839906740 1.15970288 -0.021102755 0.82441387 0.754316482
## 2146 0.204653332 -1.06444157 0.254053888 -0.02015996 0.141814540
## 2148 -1.630523178 -0.94087799 -0.883972616 -0.63439548 -1.627635513
## 2178 0.134069620 -1.18800515 -0.371059262 0.28695779 0.073758769
## 2182 0.063485909 1.15970288 1.661894188 0.82441387 0.754316482
## 2235 -2.830446281 -1.00265978 -1.022886649 -2.86099921 -2.784583625
## 2279 0.416404468 0.78901214 1.322623375 0.36373723 0.345981854
## 2281 0.416404468 -1.00265978 -1.215229157 0.36373723 0.345981854
## 2291 0.486988180 0.66544856 0.593324700 0.21017835 0.414037625
## 2322 0.557571892 0.17119423 1.213095003 0.51729611 0.482093397
## 2324 0.134069620 -3.65927675 0.005611482 -0.78795436 0.073758769
## 2325 0.486988180 0.35653960 1.774093984 0.82441387 0.754316482
## 2339 0.698739316 1.03613930 -1.260643360 0.67085499 0.618204939
## 2357 0.345820756 0.35653960 1.082195241 0.36373723 0.482093397
## 2368 0.486988180 0.41832139 1.004723953 0.36373723 0.414037625
## 2379 0.839906740 0.85079393 -1.252629089 0.74763443 0.754316482
## 2396 0.698739316 0.48010318 1.298580562 0.67085499 0.618204939
## 2405 0.628155604 0.91257572 -0.050488416 0.36373723 0.345981854
## 2410 0.134069620 -0.94087799 0.630724632 0.05661947 0.073758769
## 2443 0.063485909 0.85079393 0.782995784 0.28695779 0.277926083
## 2449 0.063485909 -1.00265978 -0.900001158 -0.48083660 0.005702998
## 2469 0.275237044 0.72723035 3.203305673 0.36373723 0.345981854
## 2496 -0.854102347 -1.43513231 -0.055831263 -0.71117492 -1.899858599
## 2519 0.204653332 -0.01415114 1.261180630 0.05661947 0.073758769
## 2526 -1.630523178 0.17119423 -0.520658990 -1.86286650 -1.899858599
## 2582 -0.289432651 -1.00265978 -0.851915531 -0.55761604 -0.334575859
## 2618 0.275237044 -1.86760484 0.614696090 0.21017835 0.209870311
## 2621 -0.642351211 -0.26127830 -0.277559432 -0.32727772 -0.674854715
## 2642 -0.783518635 -1.00265978 -1.153786412 -1.01829267 -0.810966258
## 2651 0.839906740 0.85079393 -0.560730346 0.82441387 0.754316482
## 2662 -1.630523178 -1.00265978 -1.097686513 -1.63252818 -1.627635513
## 2680 -1.983441738 -1.55869589 -0.702315803 -0.78795436 -1.491523971
## 2702 0.839906740 1.15970288 -0.536687533 0.82441387 0.754316482
## 2711 -0.712934923 -1.00265978 -1.060286581 -1.01829267 -0.742910487
## 2713 -0.077681515 -0.07593293 1.907665170 0.67085499 0.686260710
## 2728 0.839906740 1.15970288 -1.116386479 0.82441387 0.754316482
## 2738 -0.642351211 1.15970288 -1.201872038 0.59407555 -0.674854715
## 2753 -0.854102347 -1.31156873 0.660110293 -0.25049828 -0.879022029
## 2754 0.769323028 1.09792109 -0.862601226 0.74763443 0.686260710
## 2821 -0.007097803 0.17119423 0.395639345 -0.09693940 -0.062352774
## 2841 -0.218848939 0.10941244 -1.177829225 -0.32727772 -0.266520088
## 2847 0.769323028 0.17119423 -0.269545161 0.82441387 0.686260710
## 2849 0.769323028 1.15970288 -0.854586955 0.74763443 0.686260710
## Incidents_HIV Thinness_ten_nineteen_years Thinness_five_nine_years
## 1 -0.32675665 0.08510204 0.04913431
## 2 -0.32058883 -0.95960358 -0.97576220
## 7 -0.32675665 -0.54658042 -0.54673575
## 28 0.31469667 0.25517040 0.21597793
## 44 0.21601154 0.66819355 0.62116958
## 58 -0.34526011 0.35235232 0.28748234
## 75 -0.34526011 0.61960259 0.54966517
## 102 -0.22807153 0.61960259 0.59733477
## 111 -0.35142793 -0.91101262 -0.92809259
## 113 -0.30208537 2.34458164 2.36111017
## 122 8.44388396 -0.13355727 -0.11770930
## 161 3.20740444 0.44953424 0.35898675
## 167 -0.19723242 -0.57087590 -0.59440536
## 174 -0.27124627 2.70901383 2.74246701
## 183 -0.16022550 1.20269410 1.12170043
## 203 -0.24040717 -0.64376234 -0.61824016
## 217 0.17283680 0.91114835 0.85951760
## 220 -0.23423935 -0.54658042 -0.52290095
## 242 -0.25891063 -0.69235330 -0.68974457
## 269 -0.32675665 -0.81383070 -0.83275338
## 272 -0.35759575 -1.00819454 -1.02343180
## 301 -0.11705076 0.95973931 0.90718721
## 304 -0.27124627 -0.83812618 -0.80891858
## 331 -0.29591755 0.18228396 0.12063872
## 334 0.59841641 0.61960259 0.57349997
## 416 -0.33292447 -0.59517138 -0.59440536
## 427 0.08031949 0.66819355 0.64500438
## 444 -0.32675665 -0.74094426 -0.76124897
## 452 -0.28358191 -0.76523974 -0.80891858
## 474 -0.14172204 -0.30362563 -0.33222253
## 488 -0.27741409 -0.74094426 -0.73741417
## 496 -0.32675665 -0.66805782 -0.66590976
## 499 -0.17256114 0.57101163 0.52583037
## 512 -0.12938640 -0.25503467 -0.28455292
## 547 -0.27124627 -1.08108097 -1.07110141
## 557 -0.22807153 -0.44939851 -0.47523134
## 559 -0.01219781 0.23087492 0.16830833
## 580 -0.31442101 -0.23073919 -0.40372694
## 585 -0.31442101 0.93544383 0.85951760
## 591 -0.29591755 -0.25503467 -0.28455292
## 599 -0.31442101 -0.95960358 -0.97576220
## 609 -0.12938640 -0.18214823 -0.18921371
## 627 -0.35759575 -0.81383070 -0.78508378
## 629 5.79172119 0.23087492 0.16830833
## 639 -0.29591755 0.78967095 0.71650879
## 640 -0.33909229 5.38151658 5.41196490
## 651 -0.32058883 -0.47369399 -0.47523134
## 688 -0.32675665 -0.30362563 -0.30838773
## 697 -0.25274281 -0.30362563 -0.30838773
## 700 1.22136627 0.44953424 0.38282155
## 717 -0.20340024 2.00444492 2.00358813
## 728 1.78263792 0.27946588 0.33515194
## 733 -0.35142793 -0.86242166 -0.88042299
## 741 -0.20956807 0.66819355 0.62116958
## 764 1.78263792 -0.23073919 -0.26071812
## 766 -0.35759575 -0.64376234 -0.66590976
## 770 0.14816552 0.69248903 0.64500438
## 787 -0.29591755 0.42523876 0.35898675
## 810 -0.26507845 -0.71664878 -0.73741417
## 811 -0.12938640 -0.64376234 -0.66590976
## 833 -0.29591755 -0.13355727 -0.14154411
## 838 0.86363268 0.52242067 0.45432596
## 840 0.29619321 0.37664780 0.31131714
## 850 -0.34526011 -0.42510303 -0.40372694
## 852 -0.01836563 1.27558054 1.21703964
## 853 -0.27741409 0.76537547 0.74034359
## 869 -0.36993140 -0.57087590 -0.54673575
## 874 -0.30208537 -0.93530810 -0.97576220
## 901 -0.27124627 2.19880876 2.14659694
## 903 -0.36993140 0.52242067 0.45432596
## 904 -0.12938640 0.27946588 0.31131714
## 907 -0.29591755 0.18228396 0.12063872
## 957 0.90680743 0.25517040 0.23981273
## 1000 -0.28358191 0.23087492 0.16830833
## 1011 -0.29591755 3.55935561 3.57668510
## 1058 0.14199770 0.40094328 0.35898675
## 1064 -0.32675665 -0.88671714 -0.90425779
## 1067 -0.35759575 3.07344602 3.02848464
## 1068 -0.12938640 -0.25503467 -0.28455292
## 1117 -0.35142793 0.08510204 0.07296912
## 1146 -0.36993140 -0.76523974 -0.78508378
## 1150 -0.08621166 -0.66805782 -0.68974457
## 1157 -0.32675665 -0.86242166 -0.85658818
## 1158 2.21438535 0.93544383 0.88335240
## 1164 -0.20340024 -0.18214823 -0.21304851
## 1197 -0.27124627 -0.59517138 -0.66590976
## 1205 -0.32675665 -0.59517138 -0.59440536
## 1206 -0.35759575 0.44953424 0.38282155
## 1225 -0.36376358 -0.81383070 -0.80891858
## 1227 -0.31442101 1.20269410 1.12170043
## 1251 -0.12938640 -0.06067083 -0.07003970
## 1262 -0.25891063 -0.59517138 -0.64207496
## 1266 -0.30825319 -0.23073919 -0.21304851
## 1306 -0.32675665 -0.64376234 -0.59440536
## 1320 -0.15405768 -0.44939851 -0.42756174
## 1338 0.88213615 0.71678451 0.59733477
## 1358 2.44876253 0.88685287 0.83568280
## 1481 2.00467946 0.25517040 0.21597793
## 1492 -0.32675665 -0.91101262 -0.90425779
## 1503 0.33320013 0.78967095 0.71650879
## 1531 -0.35759575 -0.66805782 -0.66590976
## 1536 -0.33909229 -0.91101262 -0.92809259
## 1559 -0.28358191 -0.81383070 -0.83275338
## 1566 -0.33292447 -1.03249002 -1.04726661
## 1588 -0.36376358 -0.74094426 -0.76124897
## 1604 -0.30208537 -0.30362563 -0.28455292
## 1614 -0.34526011 -1.00819454 -1.02343180
## 1620 -0.35759575 -0.81383070 -0.80891858
## 1624 -0.33909229 0.15798848 0.07296912
## 1629 -0.28358191 0.78967095 0.69267398
## 1707 -0.35759575 2.19880876 2.09892734
## 1710 2.38708432 0.42523876 0.35898675
## 1713 -0.28974973 -0.52228495 -0.49906615
## 1716 -0.36376358 -0.61946686 -0.61824016
## 1722 -0.28974973 -0.61946686 -0.64207496
## 1732 -0.27124627 -1.05678549 -1.04726661
## 1785 -0.32675665 -0.54658042 -0.54673575
## 1801 -0.31442101 0.27946588 0.12063872
## 1810 -0.32675665 -0.91101262 -0.95192740
## 1820 -0.33909229 1.22698958 1.14553523
## 1824 -0.32058883 -0.59517138 -0.57057055
## 1844 -0.36993140 3.24351438 3.26683266
## 1875 -0.29591755 0.49812519 0.43049116
## 1882 -0.28974973 -0.37651207 -0.35605733
## 1905 -0.22807153 -0.74094426 -0.76124897
## 1948 -0.25891063 -0.91101262 -0.90425779
## 1950 -0.35759575 -0.83812618 -0.83275338
## 1976 1.78263792 0.47382972 0.43049116
## 1984 -0.35759575 -0.83812618 -0.88042299
## 1989 -0.01219781 0.27946588 0.26364754
## 2022 0.05564821 0.57101163 0.52583037
## 2077 -0.12321858 -0.78953522 -0.78508378
## 2081 -0.33292447 -0.57087590 -0.57057055
## 2118 -0.35142793 0.95973931 0.95485681
## 2120 -0.32675665 -0.64376234 -0.61824016
## 2127 -0.33909229 -0.95960358 -0.95192740
## 2128 -0.27741409 -0.25503467 -0.30838773
## 2146 -0.29591755 -0.83812618 -0.83275338
## 2148 -0.27124627 -0.74094426 -0.76124897
## 2178 -0.31442101 -0.64376234 -0.64207496
## 2182 -0.32675665 -0.71664878 -0.71357937
## 2235 0.31469667 0.88685287 0.85951760
## 2279 -0.35142793 -0.95960358 -0.95192740
## 2281 -0.29591755 -0.42510303 -0.42756174
## 2291 -0.28974973 -0.44939851 -0.42756174
## 2322 -0.16639332 -0.49798947 -0.49906615
## 2324 -0.08621166 -0.25503467 -0.26071812
## 2325 -0.31442101 -0.86242166 -0.88042299
## 2339 -0.32675665 0.30376136 0.21597793
## 2357 -0.30208537 -0.91101262 -0.95192740
## 2368 -0.29591755 -0.86242166 -0.88042299
## 2379 -0.29591755 2.63612739 2.71863220
## 2396 -0.33909229 -0.86242166 -0.85658818
## 2405 -0.21573589 0.49812519 0.47816076
## 2410 -0.28358191 1.03262574 1.02636122
## 2443 -0.34526011 -0.86242166 -0.88042299
## 2449 0.06798385 0.47382972 0.38282155
## 2469 -0.32675665 -0.64376234 -0.64207496
## 2496 -0.31442101 -0.86242166 1.21703964
## 2519 -0.35142793 -0.49798947 -0.45139654
## 2526 0.03714475 -0.15785275 -0.16537891
## 2582 0.01247347 0.23087492 0.21597793
## 2618 -0.27741409 0.83826191 0.69267398
## 2621 -0.27741409 -0.81383070 -0.83275338
## 2642 -0.31442101 -0.64376234 1.55072688
## 2651 -0.30208537 -0.13355727 -0.21304851
## 2662 -0.13555422 0.76537547 0.69267398
## 2680 -0.27124627 -1.05678549 -1.07110141
## 2702 -0.36993140 2.56324095 2.48028418
## 2711 -0.25891063 -0.76523974 -0.80891858
## 2713 -0.32058883 -0.93530810 -0.95192740
## 2728 -0.28974973 0.71678451 0.64500438
## 2738 -0.27124627 -1.08108097 -1.07110141
## 2753 3.88586468 -0.03637535 0.16830833
## 2754 -0.35142793 0.47382972 0.43049116
## 2821 -0.12938640 -0.71664878 -0.73741417
## 2841 -0.24040717 0.25517040 0.19214313
## 2847 -0.30825319 -0.66805782 -0.68974457
## 2849 -0.34526011 0.40094328 0.35898675
## attr(,"scaled:center")
## Life_expectancy Under_five_deaths
## 71.4636872 31.6804469
## Alcohol_consumption Infant_deaths
## 4.7289944 23.5586592
## Hepatitis_B Measles
## 87.1005587 80.2290503
## Alcohol_consumption.1 Polio
## 4.7289944 88.2625698
## Diphtheria Incidents_HIV
## 87.9162011 0.6097765
## Thinness_ten_nineteen_years Thinness_five_nine_years
## 4.5497207 4.5938547
## attr(,"scaled:scale")
## Life_expectancy Under_five_deaths
## 7.832270 32.217096
## Alcohol_consumption Infant_deaths
## 3.743322 21.487508
## Hepatitis_B Measles
## 14.167575 16.185999
## Alcohol_consumption.1 Polio
## 3.743322 13.024320
## Diphtheria Incidents_HIV
## 14.693831 1.621318
## Thinness_ten_nineteen_years Thinness_five_nine_years
## 4.115992 4.195546cov(data_dis)## Life_expectancy Under_five_deaths
## Life_expectancy 1.0000000 -0.9212079
## Under_five_deaths -0.9212079 1.0000000
## Alcohol_consumption 0.4487724 -0.4391376
## Infant_deaths -0.9305646 0.9899859
## Hepatitis_B 0.4397991 -0.5286901
## Measles 0.5838125 -0.5845977
## Alcohol_consumption.1 0.4487724 -0.4391376
## Polio 0.5910969 -0.6650301
## Diphtheria 0.5370849 -0.5953535
## Incidents_HIV -0.4501293 0.3122778
## Thinness_ten_nineteen_years -0.4563343 0.4789483
## Thinness_five_nine_years -0.4522485 0.4719123
## Alcohol_consumption Infant_deaths Hepatitis_B
## Life_expectancy 0.44877242 -0.9305646 0.4397991
## Under_five_deaths -0.43913759 0.9899859 -0.5286901
## Alcohol_consumption 1.00000000 -0.4692522 0.2102431
## Infant_deaths -0.46925224 1.0000000 -0.5063603
## Hepatitis_B 0.21024309 -0.5063603 1.0000000
## Measles 0.31445228 -0.5861101 0.4905367
## Alcohol_consumption.1 1.00000000 -0.4692522 0.2102431
## Polio 0.28825702 -0.6519378 0.8886645
## Diphtheria 0.27565589 -0.5814566 0.9438458
## Incidents_HIV 0.01760975 0.3409592 -0.0767645
## Thinness_ten_nineteen_years -0.45626812 0.4964201 -0.1234409
## Thinness_five_nine_years -0.45939934 0.4954018 -0.1398797
## Measles Alcohol_consumption.1 Polio
## Life_expectancy 0.5838125 0.44877242 0.5910969
## Under_five_deaths -0.5845977 -0.43913759 -0.6650301
## Alcohol_consumption 0.3144523 1.00000000 0.2882570
## Infant_deaths -0.5861101 -0.46925224 -0.6519378
## Hepatitis_B 0.4905367 0.21024309 0.8886645
## Measles 1.0000000 0.31445228 0.5571360
## Alcohol_consumption.1 0.3144523 1.00000000 0.2882570
## Polio 0.5571360 0.28825702 1.0000000
## Diphtheria 0.5305231 0.27565589 0.9296290
## Incidents_HIV -0.1843985 0.01760975 -0.1342147
## Thinness_ten_nineteen_years -0.2806768 -0.45626812 -0.2212835
## Thinness_five_nine_years -0.3048480 -0.45939934 -0.2375340
## Diphtheria Incidents_HIV
## Life_expectancy 0.5370849 -0.45012933
## Under_five_deaths -0.5953535 0.31227776
## Alcohol_consumption 0.2756559 0.01760975
## Infant_deaths -0.5814566 0.34095920
## Hepatitis_B 0.9438458 -0.07676450
## Measles 0.5305231 -0.18439848
## Alcohol_consumption.1 0.2756559 0.01760975
## Polio 0.9296290 -0.13421473
## Diphtheria 1.0000000 -0.12232658
## Incidents_HIV -0.1223266 1.00000000
## Thinness_ten_nineteen_years -0.1821165 0.08962638
## Thinness_five_nine_years -0.2107806 0.08353299
## Thinness_ten_nineteen_years
## Life_expectancy -0.45633430
## Under_five_deaths 0.47894832
## Alcohol_consumption -0.45626812
## Infant_deaths 0.49642015
## Hepatitis_B -0.12344090
## Measles -0.28067679
## Alcohol_consumption.1 -0.45626812
## Polio -0.22128352
## Diphtheria -0.18211650
## Incidents_HIV 0.08962638
## Thinness_ten_nineteen_years 1.00000000
## Thinness_five_nine_years 0.97313553
## Thinness_five_nine_years
## Life_expectancy -0.45224853
## Under_five_deaths 0.47191227
## Alcohol_consumption -0.45939934
## Infant_deaths 0.49540181
## Hepatitis_B -0.13987969
## Measles -0.30484804
## Alcohol_consumption.1 -0.45939934
## Polio -0.23753399
## Diphtheria -0.21078062
## Incidents_HIV 0.08353299
## Thinness_ten_nineteen_years 0.97313553
## Thinness_five_nine_years 1.00000000my_data1<-data_dis[,-1]
pca1 <- prcomp(my_data1)
summary(pca1)## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 2.3268 1.4661 1.1195 0.9732 0.76029 0.69642 0.30678
## Proportion of Variance 0.4922 0.1954 0.1139 0.0861 0.05255 0.04409 0.00856
## Cumulative Proportion 0.4922 0.6876 0.8015 0.8876 0.94017 0.98426 0.99281
## PC8 PC9 PC10 PC11
## Standard deviation 0.21680 0.1555 0.08864 3.576e-16
## Proportion of Variance 0.00427 0.0022 0.00071 0.000e+00
## Cumulative Proportion 0.99709 0.9993 1.00000 1.000e+00names(pca1)## [1] "sdev" "rotation" "center" "scale" "x"pca1$rotation## PC1 PC2 PC3 PC4
## Under_five_deaths 0.3770769 0.026875667 0.21508825 -0.12849342
## Alcohol_consumption -0.2731855 0.354294863 0.40288581 0.34538437
## Infant_deaths 0.3797510 0.001736199 0.22387944 -0.15621322
## Hepatitis_B -0.3072257 -0.392227253 0.18505494 -0.17930566
## Measles -0.2968243 -0.115896412 -0.06685362 0.07182463
## Alcohol_consumption.1 -0.2731855 0.354294863 0.40288581 0.34538437
## Polio -0.3489578 -0.331069284 0.10972589 -0.12290568
## Diphtheria -0.3359905 -0.355958968 0.15622617 -0.14393938
## Incidents_HIV 0.1017552 0.077988083 0.63509722 -0.52655172
## Thinness_ten_nineteen_years 0.2591817 -0.416570745 0.23049121 0.42502203
## Thinness_five_nine_years 0.2639296 -0.406231220 0.21758970 0.43528388
## PC5 PC6 PC7 PC8
## Under_five_deaths 0.1966914 0.51284804 -0.1119783725 0.02606432
## Alcohol_consumption 0.1085482 0.07751095 0.0000541613 -0.01575125
## Infant_deaths 0.1766560 0.47720009 -0.0623281063 -0.06381062
## Hepatitis_B 0.2412358 0.11404922 0.5971791767 -0.47782446
## Measles -0.7538204 0.56560550 0.0099238152 -0.00801078
## Alcohol_consumption.1 0.1085482 0.07751095 0.0000541613 -0.01575125
## Polio 0.1483225 -0.01189170 -0.7885633376 -0.30132749
## Diphtheria 0.2358806 0.10079643 0.0684134198 0.75848719
## Incidents_HIV -0.4220445 -0.35112536 0.0074111550 0.02671210
## Thinness_ten_nineteen_years -0.1151151 -0.09933940 -0.0131807329 0.23183170
## Thinness_five_nine_years -0.1052967 -0.14448392 0.0106491250 -0.21403669
## PC9 PC10 PC11
## Under_five_deaths -0.091981271 0.686248892 -7.305594e-16
## Alcohol_consumption -0.001557311 -0.014010727 7.071068e-01
## Infant_deaths 0.120641680 -0.706981820 5.551115e-16
## Hepatitis_B -0.168089884 0.031288345 -3.053113e-16
## Measles 0.022749625 0.000381374 1.387779e-16
## Alcohol_consumption.1 -0.001557311 -0.014010727 -7.071068e-01
## Polio -0.080613842 -0.014353299 5.551115e-17
## Diphtheria 0.263607391 -0.002604673 2.498002e-16
## Incidents_HIV 0.004503998 0.027553446 -1.387779e-16
## Thinness_ten_nineteen_years -0.660425909 -0.111003971 -1.110223e-16
## Thinness_five_nine_years 0.660331970 0.120721093 0.000000e+00pca1$x## PC1 PC2 PC3 PC4 PC5
## 1 -0.31668153 -1.349962667 -0.80314734 -0.598685892 0.831893787
## 2 -2.96912843 0.994966137 0.40866772 0.402701887 0.102292698
## 7 -2.34396852 0.197585647 0.16132159 0.311076427 -0.198373053
## 28 2.18763030 0.429510795 0.88158225 -0.352140966 0.935366119
## 44 0.93902882 -1.449646123 0.70146741 -0.524422777 1.110956686
## 58 -0.22645848 -1.783081029 -0.88100372 -0.424039331 -0.772405840
## 75 -0.71637284 -2.334651074 -0.86977286 -0.203696782 -0.796259310
## 102 3.15860690 0.363916458 -0.87886520 0.225125686 -0.036496686
## 111 -1.97415159 0.493237783 -0.68466065 -0.202829620 -0.225510677
## 113 0.85368988 -2.906389819 0.71808889 1.580445314 0.519730587
## 122 1.02455895 1.265415506 6.30914116 -4.308345791 -3.136848736
## 161 0.28969926 -0.384872050 3.05453273 -1.513051280 -0.772484563
## 167 -2.54483849 0.996547926 0.70701061 0.810587613 -0.009249886
## 174 2.27560836 -3.227605314 0.32812408 1.439817239 0.168153567
## 183 3.11770315 -0.247120966 1.13500155 0.590224213 1.018640276
## 203 -2.92095869 0.428647471 0.54273361 0.499317756 -0.173781339
## 217 3.53052129 1.678191122 0.91663000 1.231960563 0.140729614
## 220 3.29277537 5.138668262 -2.17398076 1.814576707 -1.462743989
## 242 -1.18670857 -0.162559408 -1.02281301 -0.630738442 -0.359404577
## 269 -1.70163633 -0.458830499 -1.22298022 -0.815739506 -0.572143210
## 272 -2.20990149 1.154321889 -0.09308159 0.178408275 0.164387710
## 301 6.24613563 1.728713909 -0.56159670 0.548506159 -0.401445448
## 304 -0.19612237 -0.409280820 -1.16132844 -1.458522481 1.010173129
## 331 2.58637701 1.014944884 -1.94730526 0.262908357 -1.173711760
## 334 2.41917300 -0.418791807 1.09815990 -0.615194314 0.870937445
## 416 -1.02312630 -0.732857493 -0.82030590 -0.942335598 0.303756888
## 427 5.56039602 1.612435701 -0.69226790 0.160862812 -0.422779474
## 444 -1.81567390 0.980103301 -0.57506562 0.367450572 -0.665290155
## 452 1.59922912 0.669485337 -1.61198327 -1.342793821 1.937495816
## 474 0.03619219 0.630496493 -0.14599313 0.001585366 -0.062678436
## 488 -0.81923439 0.562895580 -0.96880353 -0.292680274 -0.772680969
## 496 -3.26057101 1.167462296 1.03473321 1.133502773 -0.056639091
## 499 2.83905654 -0.334220096 0.02297517 -0.290716026 -0.001515220
## 512 -1.62059039 -0.081899690 0.49887201 0.144242260 0.427153636
## 547 1.36194450 0.680458049 -1.42798951 -1.627140236 0.286629108
## 557 -1.52719730 0.020313497 0.13967682 -0.080723698 0.537857609
## 559 -0.62638375 -0.612910953 0.44222338 0.143717958 -0.352481949
## 580 -1.99286733 -0.612179764 -0.15316244 -0.019042751 -0.369153847
## 585 0.67655085 -2.067725291 -0.18373062 -0.077990984 -0.141879296
## 591 -1.12106239 -1.700602864 -1.34805634 -1.031616045 -0.593430235
## 599 -1.21013698 2.070431373 -0.68830430 0.554334839 -0.514551968
## 609 -1.60991038 0.215720045 0.54365693 0.513502161 -0.011050988
## 627 -2.04591506 -0.463231610 -0.68537921 -0.657068175 -0.279287214
## 629 2.34964214 -0.186679225 4.43837181 -3.877684315 -1.735126956
## 639 -0.47913396 -2.439436134 -0.92485492 -0.113899384 -0.870658784
## 640 3.66947505 -4.620353985 2.04378712 4.354674924 -0.500339454
## 651 -2.93095678 1.615394780 1.37538523 1.627742622 0.169690408
## 688 -0.78684710 -1.028338232 -0.14906373 -0.756372520 -0.075653300
## 697 -1.91895198 0.463154512 0.53614263 0.667182529 0.318388516
## 700 1.50282892 -0.641491238 0.74249234 -1.045130030 0.246047385
## 717 2.00685974 -2.344783554 0.43773870 0.969626104 -0.114259098
## 728 -1.63085734 -0.247961881 2.13759275 -0.025456549 -1.178565213
## 733 -2.40108626 0.722599148 -0.06611978 0.183127986 -0.027599906
## 741 1.08104660 -1.030313524 0.73875216 -0.048136748 1.298434048
## 764 2.31047143 0.013266102 1.00183176 -2.284156128 0.368931488
## 766 -2.22174723 1.327696546 0.56735795 0.888485881 0.220912499
## 770 3.64216425 -0.479311808 1.53443331 -0.799551577 1.810586102
## 787 4.69070896 2.434127040 -2.17883115 0.864849382 -0.571739469
## 810 -0.85623683 -0.184574189 -1.09697754 -0.831173736 -0.241505355
## 811 -0.12733375 1.996044146 -0.64078923 0.548159187 -1.054964444
## 833 -0.86124581 -1.744649550 -1.08813695 -0.951599371 -0.490298624
## 838 0.12526309 -0.345216958 2.18058642 -0.070366820 1.204385193
## 840 1.04408075 1.126819965 1.12674480 0.771683072 0.611180695
## 850 -0.66822523 -1.305949448 -1.14105601 -1.134674010 -0.477937672
## 852 6.02885294 2.304587027 0.47902012 1.486122732 -0.287881461
## 853 -1.52506291 -1.216007986 0.65416212 1.095467062 -0.349971359
## 869 -2.25019450 0.107567027 0.42979678 0.200289859 0.032420173
## 874 -3.04035821 0.900180440 0.45698345 0.370611001 0.093300739
## 901 -0.05222125 -3.490550229 0.03707943 1.291864502 -1.195447356
## 903 1.95036071 -1.424789363 -0.22871806 -0.805299770 1.197844352
## 904 -0.51336291 -0.289519297 0.29593479 0.527444507 0.167977720
## 907 -1.29694128 -1.668637217 -0.73357205 -0.252793019 -0.718751450
## 957 1.18738494 1.092764260 1.40591268 0.199388116 0.397185823
## 1000 -0.66156539 -0.751539841 0.14292275 0.158115698 0.563502534
## 1011 5.32878986 -2.401458300 0.70369538 2.287361395 0.177764436
## 1058 1.48710837 -0.742226034 0.01286762 -0.586217761 0.764647443
## 1064 -2.45478012 0.851427148 -0.07873957 0.243665418 -0.087895980
## 1067 5.50077497 -1.417729603 0.13609934 2.105446580 0.478141268
## 1068 -1.53162813 -0.017761057 0.14839424 0.206559554 -0.363787576
## 1117 0.76439014 -0.146404898 -1.42891541 -0.057523286 0.150006545
## 1146 -2.80083072 1.381987189 0.53415495 0.973058091 -0.163698886
## 1150 -0.79915907 -0.010817464 -0.79140195 -0.762722425 -0.062975381
## 1157 -2.85056490 0.845667542 0.55517459 0.402363004 0.582617991
## 1158 6.04272275 4.584466142 1.66685679 1.386795168 -1.985945000
## 1164 -2.05764639 0.289134659 0.88343119 0.740047871 0.227035856
## 1197 -2.25333129 0.747978550 0.02014628 0.505477486 -0.292007278
## 1205 -1.23666034 -0.198924088 -0.94118558 -0.427123199 -0.639066865
## 1206 -0.41067192 -2.175750108 -0.76107486 -0.492611315 -0.455430237
## 1225 -2.78734156 0.906415156 0.43378701 0.561440772 -0.065223393
## 1227 2.14501338 -1.632823007 -0.30388795 0.055463751 1.046811281
## 1251 -1.74052388 -0.003555485 1.10217406 0.562750961 0.610699312
## 1262 -0.97017822 0.072977934 -0.69472388 -0.442512066 -0.091599498
## 1266 -0.20121509 -1.294304165 -0.77166660 -1.024049928 -0.203880251
## 1306 -2.56430328 1.297250347 0.73170180 1.034007848 0.207345474
## 1320 -1.11068982 0.638971264 -0.11587529 0.266831535 -0.449848495
## 1338 2.17119855 -0.246402187 0.38523010 -0.406343445 -0.016176784
## 1358 1.36229689 -1.114572438 1.90334063 -1.279652428 -0.220656026
## 1481 1.45901867 -0.031909076 1.63230874 -1.329370396 0.119945193
## 1492 -2.31330406 0.460944946 -0.17039720 -0.115155318 0.069419605
## 1503 2.31718889 -0.732662273 0.33073487 -0.466181903 2.137534169
## 1531 -1.80272326 1.205731666 -0.21804899 0.674289928 -0.521881056
## 1536 -2.25376284 0.267372182 -0.28220995 -0.310396505 0.452555213
## 1559 -1.05100106 -0.534589757 -0.51983655 -1.210511248 0.596069021
## 1566 -2.77237473 1.352804029 0.44417813 0.455026867 0.440291201
## 1588 -2.53401021 0.898094046 0.24718480 0.567980321 -0.172870971
## 1604 -0.82975262 -0.275440625 0.07587831 -0.275849394 1.265374443
## 1614 -2.51055955 1.220083690 0.13431631 0.320601691 0.256680421
## 1620 1.01910370 1.223701475 -1.76737067 -0.569242632 -0.663141467
## 1624 -1.00853561 -1.791384192 -0.97513154 -0.500028129 -0.380484512
## 1629 3.71582461 -0.074123817 -0.65197710 -0.065055480 0.285697121
## 1707 3.74239277 -1.164210421 -0.55786660 1.608048691 -1.820714392
## 1710 1.91362980 -0.274503010 2.12318875 -1.681022700 0.896482325
## 1713 -1.60662338 -0.805455908 -0.72299626 -0.621465523 -0.442756698
## 1716 -1.93732350 0.350740630 -0.13671278 0.153683615 0.168155161
## 1722 -0.84026303 0.231163337 -0.26808412 -0.436573674 0.813613187
## 1732 1.16212641 1.433408494 -1.70191275 -0.968600169 0.254856493
## 1785 -0.47663697 1.025469157 -1.05607848 0.258136936 -0.742085566
## 1801 -0.94955845 -1.968031171 -0.98279166 -0.506880141 -0.675853595
## 1810 -2.41492547 1.177877713 0.17344372 0.381585610 0.260977489
## 1820 3.92661796 -0.404306737 -0.47605642 0.376933594 0.177084056
## 1824 -1.43993081 -0.346416890 -0.69407792 -0.455381989 -0.451296005
## 1844 1.69820022 -4.406017107 0.59565018 1.782035643 -0.764329394
## 1875 6.59614184 2.315820031 -1.04458743 0.174425857 -0.351023982
## 1882 -1.30774900 -1.142128120 -0.67036895 -0.739487982 -0.419355065
## 1905 -1.89833609 0.167408185 -0.34352917 -0.261043108 -0.204684370
## 1948 -2.30644506 0.574429692 0.01905035 -0.082331605 0.186859617
## 1950 -2.59646884 1.450200128 0.43055609 0.836573846 -0.057078313
## 1976 4.53169828 2.073427746 0.83584311 -0.414881579 -0.943942499
## 1984 -2.10646454 1.275419845 0.11143819 0.463405547 0.440416495
## 1989 -0.58614097 -0.778389476 0.98841758 0.079547010 0.379888288
## 2022 -0.79409511 -1.676369297 -0.11141389 0.002407280 -0.757276204
## 2077 2.64218339 1.992003061 -1.52605557 -0.747584660 -0.011872172
## 2081 -1.38882328 -0.841781227 -1.28234681 -0.803116364 -0.340570648
## 2118 0.33454855 -2.407209328 -0.63039784 -0.119301085 0.648096671
## 2120 -2.63303074 0.872405901 0.56293027 0.750713647 0.002036702
## 2127 -2.00145216 0.764476989 -0.36744844 -0.093769311 0.259535844
## 2128 -1.94849639 -0.833567994 -0.40489627 -0.146166600 -0.512357179
## 2146 -0.78125203 0.829410978 -0.45366467 -0.372168646 1.055493434
## 2148 1.57087685 1.505451171 -1.80649851 -0.563456298 -0.094997705
## 2178 0.08846912 0.205797384 -0.59974557 -0.826784482 1.213193416
## 2182 -2.87343003 1.016043292 0.57450210 0.813597574 -0.223785654
## 2235 6.35821635 1.827533399 -0.15657570 0.233557080 -0.467308829
## 2279 -2.54684256 1.173077623 0.13595965 0.422039593 -0.048764272
## 2281 0.17282370 -0.831395317 -1.21520850 -1.230850894 0.864797615
## 2291 -1.64070237 0.254811956 -0.05809804 0.247758894 -0.153176413
## 2322 -1.91634149 0.659708977 0.63377188 0.430587105 0.436389846
## 2324 0.92049939 0.805601646 -0.10304428 -0.288902441 2.672186299
## 2325 -2.96750527 1.149913166 0.69975509 0.639388195 0.507657416
## 2339 -0.60278148 -1.985657121 -1.12547205 -0.536244499 -0.772837701
## 2357 -2.21541847 1.018297219 0.06728992 0.182891104 0.251965100
## 2368 -2.04706765 0.880565331 0.12412467 0.116093768 0.255718012
## 2379 1.11464260 -4.055773180 0.34981061 1.270783390 -0.846435077
## 2396 -2.70339483 0.803367845 0.30063829 0.342529970 0.316815324
## 2405 -0.70987363 -1.060785354 0.03757806 0.455420082 -0.559176218
## 2410 0.94518080 -0.390883710 1.23575980 1.138443798 1.084539277
## 2443 -2.11280844 0.901106043 -0.37178855 0.222699816 -0.368485327
## 2449 2.16547870 -0.697774054 0.11645129 -0.688994830 0.876161649
## 2469 -3.37180348 2.311981805 1.77053656 2.007886985 0.280362664
## 2496 1.64393418 1.212078022 -0.63113707 0.710592422 0.399869360
## 2519 -1.61964174 1.113406352 0.32126859 0.797751338 0.345179388
## 2526 2.90632839 1.713852227 -0.72287481 -0.076228550 -0.866219667
## 2582 2.71382469 -0.200442790 0.15546541 -0.848487640 0.992239867
## 2618 1.80905687 -0.191788970 1.73233102 0.450851480 2.354917166
## 2621 -0.06506489 1.075380569 -1.22797665 -0.380023873 -0.112091892
## 2642 2.56379348 -0.137541417 -0.93260837 -0.133436188 0.288777640
## 2651 -1.00442428 -1.254498358 -0.49339361 -0.626619478 -0.163726425
## 2662 4.54322815 0.554402210 -0.34949618 -0.024734840 0.217558289
## 2680 1.35920403 2.095398398 -1.96425344 -0.594632580 0.281426806
## 2702 -0.12161926 -3.510233066 0.42856251 1.924316923 -1.160326900
## 2711 1.96940109 0.900506040 -1.25413700 -1.250842678 0.658947236
## 2713 -2.66828247 1.651394156 0.68676729 0.759528403 0.722083124
## 2728 -0.77730852 -2.400569884 -0.82280643 -0.095238178 -0.922809675
## 2738 -0.51418381 0.156633223 -2.12228298 -1.220132236 -1.232874290
## 2753 1.24736421 1.604676707 2.87621995 -1.371142382 -0.902437035
## 2754 -0.70602280 -1.944481489 -0.64508420 -0.150365381 -0.668517881
## 2821 -0.87731600 0.894509699 -0.28072550 -0.147475543 0.005135308
## 2841 1.92237151 -0.730346959 -0.57527156 -0.730994824 0.012980408
## 2847 -1.31143477 -0.506163578 -0.54292139 -0.834241203 0.429620060
## 2849 -1.02492282 -1.894751261 -0.82176779 -0.107113756 -0.826880865
## PC6 PC7 PC8 PC9 PC10
## 1 -1.014187e+00 0.0191654457 -0.0085256179 -0.0689819974 0.0352715808
## 2 2.818884e-01 0.0981887370 -0.1044396478 -0.0419968989 0.0305279170
## 7 3.556468e-01 0.0706971544 -0.0905103420 -0.0174672252 0.0295722795
## 28 8.560820e-01 0.2315307689 0.1401156617 0.0160529509 0.1129982422
## 44 5.750660e-02 -0.1640578203 -0.0162534639 -0.0432902080 0.1012599961
## 58 4.869355e-01 -0.0065168283 -0.0192507501 -0.0153989104 -0.0470251860
## 75 -4.995075e-02 0.0206514501 -0.0087360812 -0.0479514782 0.0560147122
## 102 -2.231903e-01 0.2157994193 0.1225252774 -0.0129597262 0.0095393683
## 111 -1.102175e-01 -0.1681840027 0.1817154515 0.0388634767 0.0491089981
## 113 -1.232608e+00 -0.0346255010 -0.0044547252 -0.0255524047 0.0319823255
## 122 -1.795041e+00 0.3033867948 0.2599504802 0.1281182287 0.0549449419
## 161 -4.240815e-01 -0.1901074821 -0.0115349613 -0.0227954543 -0.0650544310
## 167 1.210706e-01 0.1321484465 -0.0314745447 -0.0271191609 0.0140020310
## 174 -1.051137e+00 0.0259116833 0.0529255487 0.0220177910 -0.0419685092
## 183 1.229983e+00 -0.0496708258 0.0359734342 0.0291497019 -0.2606791212
## 203 3.718439e-01 0.0700589427 -0.1143870343 -0.0069147667 0.0508859408
## 217 5.623819e-01 0.1984062829 0.1211810180 -0.0195334501 0.0541460142
## 220 -2.177070e+00 -0.6825978962 -0.2858431806 -0.2041546063 -0.0743068471
## 242 -1.105500e-01 0.1295388383 -0.0237587744 -0.0169334142 0.0449821390
## 269 3.930237e-02 0.1654558126 -0.0631005672 -0.0438575585 0.0851574019
## 272 6.111064e-05 0.1492412891 -0.0666192466 -0.0450437813 0.0211857001
## 301 1.196154e+00 -0.2344444266 0.0525786540 -0.0788876172 0.3374951148
## 304 -4.684446e-01 0.7384514576 0.2442054267 0.0733444443 -0.0099046676
## 331 -7.133180e-01 -0.4683398458 -0.0753045551 -0.0986249656 -0.1082081641
## 334 7.809376e-01 -0.0132079203 0.0768806257 0.0001427998 0.1222609472
## 416 4.369162e-02 -0.0654557056 -0.0815690888 -0.0139361184 -0.0221163303
## 427 8.031676e-01 0.5408004317 0.3119211149 0.0413152758 0.1518488500
## 444 -1.178711e-01 -1.2198074014 0.9679241908 0.3258806614 -0.0067824738
## 452 -1.829959e+00 -0.2483056903 -0.0799655592 -0.1357514244 -0.0746122476
## 474 3.534096e-01 -0.2198896291 0.0615475757 0.0316789402 -0.1284963097
## 488 3.012885e-01 -0.0514819517 0.1450591403 0.0655862182 -0.0320521286
## 496 4.788156e-01 0.1016628995 -0.1255779351 -0.0257786478 0.0219285124
## 499 1.755152e+00 0.3963798577 0.2192618471 0.0652893168 0.1269160964
## 512 4.457395e-02 0.0548242541 -0.0621359080 -0.0250388448 -0.0610347957
## 547 8.088393e-01 0.0857972058 -0.1801706572 -0.0183746666 -0.1279804530
## 557 -7.672738e-02 -0.0957160124 -0.1175694718 -0.0482701522 -0.0487325168
## 559 7.209675e-01 0.1313279348 0.0060563676 0.0064872837 -0.0949987203
## 580 3.753186e-01 0.0282079546 -0.0418720030 -0.1245809046 0.0293063918
## 585 5.822890e-01 -0.1239189723 -0.0240332544 -0.0290972204 -0.0042350274
## 591 -3.322494e-02 0.0368557450 -0.0225618784 -0.0283319565 0.0750485474
## 599 -3.930864e-01 -1.3548488698 1.1608370387 0.3817775225 -0.0580505566
## 609 1.467079e-01 -0.3390043717 -0.2266226638 -0.0549017300 -0.0588181459
## 627 4.004102e-01 0.0341040234 -0.0863761502 0.0124558226 0.0267256356
## 629 8.835867e-02 0.1516371489 0.2294977301 0.1257271435 -0.0908673616
## 639 -2.832884e-01 0.1061171176 0.0331005767 -0.0501183528 0.0766238640
## 640 -1.226474e+00 0.0317572953 0.0846236129 0.0324204171 -0.0596497398
## 651 2.572545e-01 0.1837721599 -0.1456537385 -0.0470801340 -0.0020519798
## 688 1.403351e+00 -0.1609687234 -0.1181123105 0.0562024716 -0.1877879821
## 697 -1.104996e-01 0.8239344762 0.2050467219 0.0415137039 0.0365789612
## 700 -5.632373e-01 -0.0618874151 0.0440960433 -0.0546520032 0.0801117449
## 717 1.059900e-01 -0.0895025863 -0.0014227789 0.0295919993 -0.0954695693
## 728 -2.844617e-01 0.0869824167 -0.0837995355 0.0332435045 0.0397854669
## 733 1.051483e-01 0.0772711785 -0.0421976665 -0.0304432478 0.0335110690
## 741 5.213340e-01 -0.2318565165 -0.0594561994 -0.0365060687 0.0282195081
## 764 3.464295e-01 -0.2709472754 -0.4151503851 -0.1201745329 -0.0544980699
## 766 9.183721e-02 0.1881425346 -0.1103832736 -0.0580256201 -0.0095339108
## 770 2.306326e+00 -0.5166386035 -0.0836061939 0.0267289386 -0.0248041187
## 787 -1.792454e+00 0.0901182431 0.0883757265 -0.1628366038 0.1136783759
## 810 1.544492e-02 0.0427651414 -0.0422381087 -0.0275704584 -0.0033844677
## 811 7.071321e-02 0.4055460276 0.0628099179 -0.0083892387 -0.0565406097
## 833 2.515219e-01 -0.0152077907 -0.0427673717 0.0028947795 0.0151342836
## 838 9.730063e-02 -0.1097289225 -0.0275932947 -0.0409084212 0.0027803420
## 840 -1.436496e-01 0.1142497055 0.0315617675 -0.0506114257 -0.0414776300
## 850 6.948705e-01 -0.1478281930 -0.1063868125 0.0341641745 -0.0776696997
## 852 1.341996e+00 0.5089624620 0.3022011543 0.0212696726 0.1634153071
## 853 3.551755e-02 0.0218726910 -0.0665908539 -0.0281742055 0.0173440828
## 869 8.485373e-01 -0.0240928863 -0.1313530259 0.0234886427 -0.0596607571
## 874 3.329426e-01 0.0829671355 -0.1046148239 -0.0558311423 0.0258880548
## 901 -4.439945e-01 0.0263742019 0.0126684064 -0.0380704719 0.0791606882
## 903 6.358664e-01 -0.2930765775 -0.0568845165 -0.0225580715 -0.1249349800
## 904 -2.759046e-01 0.2348904072 0.3190015235 0.1301192586 -0.0588541036
## 907 1.610569e-02 0.0443787419 -0.0252305405 -0.0493233658 0.0669616555
## 957 -2.484838e-01 -0.3641808685 -0.1383139681 -0.0633199199 -0.0029356023
## 1000 -2.131401e-01 -0.0171477116 -0.0440603162 -0.0611413550 -0.0218877433
## 1011 -5.316456e-01 -0.0190610332 0.0895204559 0.0609477934 -0.2736441574
## 1058 -1.555954e-01 -0.0807315090 0.0068513323 -0.0362469519 0.0136319584
## 1064 2.007768e-02 -0.2778844337 0.2183500625 0.0609010521 0.0306658699
## 1067 -1.190099e+00 -0.0059518422 0.1111629375 -0.0428124505 -0.1227330579
## 1068 3.113119e-01 0.0672368542 -0.0595412633 -0.0205561322 -0.0243477646
## 1117 -1.473494e+00 0.2657583407 0.0800977689 -0.0632408839 0.0553226298
## 1146 2.606432e-01 -0.1648566775 0.1356938959 0.0390999613 0.0096387471
## 1150 -2.004295e-01 0.1011688791 -0.0172283538 -0.0282618284 -0.0058656785
## 1157 -1.089838e-02 0.0184645684 -0.0811058926 -0.0274483632 0.0306195603
## 1158 -2.934802e-01 0.4455976971 -0.9522241642 -0.3925738659 -0.1352882152
## 1164 2.499145e-01 0.0267797683 -0.0981371116 -0.0304662014 -0.0665428099
## 1197 -7.237859e-02 -0.6153612405 0.3065637796 0.0558081286 0.0195963633
## 1205 2.310210e-01 0.1137514717 -0.0866986176 -0.0205357622 0.0146494317
## 1206 3.192693e-01 -0.0543148740 -0.0323199217 -0.0256316047 -0.0319716659
## 1225 4.454469e-01 0.0962582672 -0.1078584041 -0.0186992013 0.0158463243
## 1227 -7.204629e-01 0.1662873351 0.1301334437 -0.0590362418 0.0450712873
## 1251 2.609992e-01 -0.0502311461 -0.1152477328 -0.0102733923 -0.1012251508
## 1262 -1.222868e-02 0.1013010108 -0.0241218546 -0.0422219766 -0.0195516904
## 1266 8.988714e-01 -0.0953394418 -0.0749067967 0.0585331490 -0.1435855176
## 1306 -3.277105e-03 0.1470917306 -0.1001522855 -0.0072675435 0.0267707618
## 1320 1.831855e-01 0.1411313956 -0.0945319624 -0.0074341621 -0.0290695654
## 1338 -6.043827e-01 0.0440902288 0.0896983027 -0.0830745837 0.0149648568
## 1358 -1.188904e+00 -0.0789951127 0.0608861763 -0.0426636236 0.1098089473
## 1481 -4.879581e-01 -0.1455215568 0.0130659654 -0.0330285525 0.0803582503
## 1492 1.437088e-01 -0.0081357478 -0.0208666113 0.0025148778 0.0230026903
## 1503 -1.691399e+00 0.2776957681 0.1833700366 -0.0720535343 0.0234084505
## 1531 2.674455e-04 -0.0920065647 0.1883091671 0.0567772669 0.0207517115
## 1536 -2.139169e-01 -0.0698758629 0.0207747980 -0.0166993784 0.0400640264
## 1559 5.290316e-01 -0.0995308156 -0.0894732838 -0.0058588398 -0.0623270293
## 1566 3.276644e-02 0.1180411439 -0.0969491395 -0.0508668432 0.0162257143
## 1588 3.016097e-01 0.1297797351 -0.0832604159 -0.0373525677 0.0182653086
## 1604 -4.248239e-01 -0.0368145640 -0.0792571887 -0.0130034884 -0.0829389538
## 1614 -5.985071e-03 -0.2313652498 0.2279620517 0.0650023667 0.0044116277
## 1620 5.859332e-02 0.5616766813 0.1654454685 0.0436098933 -0.0759478105
## 1624 -2.765013e-01 0.0376596471 -0.0091129525 -0.0747355024 0.0683649021
## 1629 4.720902e-01 0.3397961771 0.2204975101 -0.0221102177 0.0703764701
## 1707 6.355769e-01 0.5118927596 0.2582217570 0.0323627569 -0.0973182283
## 1710 -1.016536e+00 -0.1706766399 0.0417041436 -0.0582761337 0.0737101633
## 1713 3.341410e-01 0.0334337421 -0.0689095005 0.0152534054 0.0172148074
## 1716 -1.267264e-01 0.0592634098 -0.0341711360 -0.0206801671 0.0291339310
## 1722 -1.841153e-01 0.0254839260 -0.0541003001 -0.0350672074 -0.0634420283
## 1732 -5.073230e-01 0.5866089741 -0.1135601385 -0.0728080595 -0.0720345396
## 1785 -3.492572e-01 0.7656120271 0.2062941314 0.0224238357 0.0469051316
## 1801 -1.815373e-02 0.0245937335 0.0055944191 -0.1108444977 0.0546991327
## 1810 -7.010910e-02 -0.2380027101 0.1846743974 0.0287907818 0.0041142003
## 1820 3.594187e-01 -1.0340355929 -0.2723712630 -0.2095318301 0.3819172993
## 1824 3.786243e-01 -0.0467734127 -0.1062654811 0.0070621778 -0.0143776991
## 1844 -1.177495e-01 -0.1787390742 -0.0294384084 0.0397805760 -0.0388773348
## 1875 1.555873e+00 -0.1616615043 0.0735464827 -0.0540484433 0.1879450412
## 1882 5.838852e-01 -0.0252664088 -0.0791441226 0.0318116863 -0.0380279017
## 1905 1.515683e-01 0.0913370609 -0.0596217792 -0.0303740570 0.0234468653
## 1948 1.245884e-01 0.1239285296 -0.1202954564 -0.0339996242 0.0214175881
## 1950 1.978830e-01 0.0074731093 0.2013279565 0.0735493931 0.0069774895
## 1976 -6.584067e-02 -0.5520153311 -0.1210381721 -0.0584083270 -0.1235332219
## 1984 -3.244275e-01 -0.0721850209 0.1049598868 -0.0163530798 0.0101252771
## 1989 8.878330e-01 -0.2282057862 -0.1239521462 -0.0009414665 -0.0228085354
## 2022 -5.908365e-02 -0.0309688029 -0.0427127903 -0.0320021869 0.0137602426
## 2077 1.044750e-02 1.2156468152 0.7538621326 0.2236524740 -0.1223633084
## 2081 -3.386206e-01 0.1118634344 -0.0213680928 -0.0307223106 0.1024532031
## 2118 -1.174872e+00 -0.0117477402 0.0009970070 -0.0424583187 0.0384463778
## 2120 2.681489e-01 0.3531106447 0.0889496700 0.0499744958 0.0254132283
## 2127 -2.785200e-01 0.1448565633 -0.0573343724 -0.0375622243 0.0473383893
## 2128 1.451521e-01 0.0581897572 -0.0511826077 -0.0516328497 0.0706167111
## 2146 -7.239537e-01 0.2257558940 0.0132084053 -0.0362531250 0.0164759392
## 2148 -7.873274e-01 -0.5826119086 -0.2479147639 -0.1268836234 -0.1058810852
## 2178 -3.580384e-01 -0.1649548762 -0.1046083531 -0.0316731284 -0.1254377363
## 2182 4.230152e-01 -0.4009308522 0.2455881974 0.1107410995 -0.0027798329
## 2235 1.269428e+00 -0.1400512967 0.0558274159 0.0356948739 -0.1633646015
## 2279 1.934713e-01 0.1487092564 -0.0845561293 -0.0251337256 0.0268701064
## 2281 -6.864262e-01 0.0143140136 -0.0103956804 -0.0272303068 -0.0268470210
## 2291 1.196915e-01 0.2739842740 -0.0015068662 0.0177670334 -0.0002561739
## 2322 3.277504e-02 0.0548581494 -0.0892768229 -0.0240550349 -0.0310203996
## 2324 -2.243632e+00 0.7251936138 0.2595341405 -0.0245488338 -0.0578817969
## 2325 -1.011721e-02 -0.1422408499 0.0521548440 0.0029881468 0.0169222765
## 2339 1.538454e-02 0.0357288169 0.0009947462 -0.0563238780 0.0382209786
## 2357 -3.207787e-03 0.0939460643 0.0709528615 -0.0125909181 0.0063623614
## 2368 1.841762e-01 0.1452648758 -0.0593131970 -0.0261741338 -0.0280959685
## 2379 7.102129e-03 -0.0521340605 -0.0107387501 0.0910650462 -0.0197196148
## 2396 7.344252e-03 0.0965996137 -0.0979789701 -0.0359103366 0.0405153851
## 2405 2.214869e-01 0.1801704543 -0.1351611097 -0.0407213320 -0.0220086379
## 2410 2.002430e-01 -0.1042538863 -0.0625348633 0.0044113708 -0.1522619636
## 2443 1.763155e-02 0.0038362532 0.0826481066 0.0047333311 0.0455380966
## 2449 4.895431e-01 0.1730462668 0.1398680652 -0.0235490263 0.0748169847
## 2469 3.164449e-01 0.0687082962 -0.0662674207 -0.0153101983 -0.0146727524
## 2496 -1.117236e+00 -0.0637806783 -1.2753941465 1.0444535264 0.1843462066
## 2519 -2.543550e-01 0.2058983044 -0.0978352758 -0.0193961904 0.0040863183
## 2526 9.451392e-01 0.1498744029 -0.1416733630 -0.0207838269 -0.1540861599
## 2582 1.059183e+00 -0.0944326640 0.0177346651 0.0432600759 -0.1031446610
## 2618 9.053508e-01 -0.3563442064 -0.0524298208 -0.1450216656 0.2586353884
## 2621 -5.188351e-01 -0.0878751014 -0.0957347116 -0.0739659097 -0.0297665213
## 2642 -2.325477e-01 0.1720180631 -0.4212177150 1.4836889290 0.0355660502
## 2651 5.248266e-01 -0.0574001266 -0.0572940427 -0.0373579382 -0.0484324511
## 2662 9.835864e-01 -0.2032389669 0.0382351542 -0.0674324003 0.2112863975
## 2680 -1.380989e+00 -0.6125105600 0.0776528608 -0.0457624936 -0.0738878113
## 2702 -4.707935e-01 0.0308689922 0.0125938634 -0.0619783536 0.0715230402
## 2711 3.334529e-01 0.1521552981 0.0807830092 -0.0207849371 0.0118408084
## 2713 -2.414427e-01 -0.3746152842 0.3125788947 0.0840354207 -0.0027738249
## 2728 -1.630951e-01 0.0400198083 -0.0009558874 -0.0539135973 0.0803440763
## 2738 8.617866e-02 -0.7817101130 -0.3614088145 -0.0993672210 0.0028663556
## 2753 -2.022166e+00 -0.3852086379 -0.1453136221 0.0679293087 0.0241191583
## 2754 2.243954e-01 -0.0009111139 -0.0313695950 -0.0190961008 0.0055644203
## 2821 1.614303e-02 0.1348057254 -0.0292102467 -0.0232686399 -0.0551640339
## 2841 1.095172e+00 -0.1016184582 -0.0157045469 0.0332134708 -0.2747119899
## 2847 1.263836e-01 -0.0800154674 -0.0931307258 -0.0297913012 -0.0321636531
## 2849 -6.115820e-02 0.0573904909 -0.0166634637 -0.0359602634 0.0735911069
## PC11
## 1 2.275660e-16
## 2 1.206511e-16
## 7 7.565225e-17
## 28 -6.514876e-16
## 44 -3.608457e-16
## 58 3.799828e-16
## 75 5.463842e-16
## 102 -1.120148e-16
## 111 4.100782e-16
## 113 -1.932439e-16
## 122 -1.361783e-15
## 161 -6.191760e-16
## 167 -2.084572e-16
## 174 -9.226490e-17
## 183 -4.391416e-16
## 203 1.169831e-16
## 217 -8.101949e-16
## 220 7.977565e-17
## 242 4.201977e-16
## 269 5.068873e-16
## 272 2.486920e-17
## 301 -8.464312e-16
## 304 2.882163e-16
## 331 3.311090e-16
## 334 -7.449536e-16
## 416 3.082096e-16
## 427 -5.047170e-16
## 444 8.956495e-16
## 452 5.285160e-17
## 474 1.927085e-16
## 488 4.745036e-16
## 496 8.913895e-17
## 499 -3.203601e-16
## 512 -7.812842e-17
## 547 2.869391e-16
## 557 9.394049e-17
## 559 1.401725e-16
## 580 2.479333e-16
## 585 8.892227e-17
## 591 6.366408e-16
## 599 8.803988e-16
## 609 4.234633e-17
## 627 4.019279e-16
## 629 -9.234076e-16
## 639 4.951306e-16
## 640 -5.756289e-16
## 651 -4.624348e-16
## 688 4.242707e-16
## 697 -1.965198e-16
## 700 -3.301237e-16
## 717 4.930193e-17
## 728 -4.198169e-16
## 733 1.826389e-16
## 741 -3.613099e-16
## 764 -4.684931e-16
## 766 -3.685336e-17
## 770 -8.613082e-16
## 787 -3.006814e-16
## 810 3.512395e-16
## 811 1.551125e-16
## 833 5.121318e-16
## 838 -5.285591e-16
## 840 -5.900446e-16
## 850 6.071067e-16
## 852 -1.018651e-15
## 853 -3.432686e-17
## 869 1.268662e-16
## 874 3.586929e-16
## 901 1.387410e-16
## 903 6.169295e-17
## 904 1.232373e-16
## 907 4.215552e-16
## 957 -4.476810e-16
## 1000 3.716568e-18
## 1011 -2.499057e-16
## 1058 -6.391428e-17
## 1064 3.354596e-16
## 1067 -4.387346e-16
## 1068 1.186396e-16
## 1117 1.128351e-16
## 1146 2.854397e-16
## 1150 2.612488e-16
## 1157 1.532426e-16
## 1158 -1.519183e-15
## 1164 1.807300e-17
## 1197 3.979341e-16
## 1205 4.018235e-16
## 1206 4.559552e-16
## 1225 3.112409e-16
## 1227 -8.537168e-17
## 1251 -1.852049e-16
## 1262 2.632458e-16
## 1266 4.608457e-16
## 1306 -2.206528e-16
## 1320 1.100894e-16
## 1338 -2.607719e-16
## 1358 -6.304949e-16
## 1481 -6.007854e-16
## 1492 2.826458e-16
## 1503 -5.820058e-16
## 1531 2.563860e-16
## 1536 2.158603e-16
## 1559 1.973674e-16
## 1566 8.793009e-17
## 1588 -7.244297e-17
## 1604 3.621653e-18
## 1614 3.472521e-16
## 1620 3.764118e-16
## 1624 4.857554e-16
## 1629 -1.704757e-16
## 1707 4.238948e-17
## 1710 -7.797443e-16
## 1713 4.221485e-16
## 1716 1.018662e-16
## 1722 9.070320e-17
## 1732 1.438807e-16
## 1785 2.222188e-16
## 1801 4.688449e-16
## 1810 2.058722e-16
## 1820 -6.122000e-16
## 1824 4.135059e-16
## 1844 1.092102e-16
## 1875 -5.266040e-16
## 1882 4.272269e-16
## 1905 2.352998e-16
## 1948 8.543436e-17
## 1950 2.790335e-16
## 1976 -5.656427e-16
## 1984 1.382726e-16
## 1989 -2.007200e-16
## 2022 2.358343e-16
## 2077 1.364473e-16
## 2081 5.020323e-16
## 2118 1.551481e-16
## 2120 8.213137e-17
## 2127 9.368026e-17
## 2128 3.062102e-16
## 2146 -2.586533e-17
## 2148 3.442385e-16
## 2178 9.394982e-17
## 2182 5.811478e-16
## 2235 -4.414287e-16
## 2279 3.988102e-17
## 2281 3.059028e-16
## 2291 9.417572e-17
## 2322 -1.055445e-16
## 2324 -4.143806e-16
## 2325 1.515307e-16
## 2339 4.253346e-16
## 2357 6.163937e-17
## 2368 1.494107e-16
## 2379 3.113952e-16
## 2396 1.124296e-16
## 2405 1.159486e-16
## 2410 -3.867885e-16
## 2443 3.400401e-16
## 2449 -4.203744e-16
## 2469 -6.647420e-16
## 2496 -2.567192e-16
## 2519 -9.641828e-17
## 2526 -6.602422e-17
## 2582 -1.418943e-16
## 2618 -1.156208e-15
## 2621 2.751728e-16
## 2642 1.890674e-16
## 2651 3.464543e-16
## 2662 -6.743913e-16
## 2680 3.492692e-16
## 2702 1.119762e-16
## 2711 1.008286e-16
## 2713 1.349541e-16
## 2728 4.168689e-16
## 2738 6.881999e-16
## 2753 -8.242300e-16
## 2754 3.201172e-16
## 2821 1.320742e-16
## 2841 2.533562e-16
## 2847 3.063847e-16
## 2849 4.383755e-16library(factoextra)
fviz_eig(pca1,addlabels=TRUE) #represent the proportion values
pca<-pca1$x[,1:6]
head(pca)## PC1 PC2 PC3 PC4 PC5 PC6
## 1 -0.3166815 -1.3499627 -0.8031473 -0.5986859 0.8318938 -1.0141867
## 2 -2.9691284 0.9949661 0.4086677 0.4027019 0.1022927 0.2818884
## 7 -2.3439685 0.1975856 0.1613216 0.3110764 -0.1983731 0.3556468
## 28 2.1876303 0.4295108 0.8815823 -0.3521410 0.9353661 0.8560820
## 44 0.9390288 -1.4496461 0.7014674 -0.5244228 1.1109567 0.0575066
## 58 -0.2264585 -1.7830810 -0.8810037 -0.4240393 -0.7724058 0.4869355res1 <- cor(pca, method="pearson")
corrplot::corrplot(res1, method= "color", order = "hclust")
biplot(pca1, col = c("gray", "black"))
fviz_pca_var(pca1, col.var = "contrib")
fviz_pca_var(pca1, select.var = list(contrib = 6))
fviz_pca_ind(pca1, col.ind = "#00AFBB")
fviz_contrib(pca1, choice = "ind", axes = 1:2) + coord_flip()
fviz_pca_ind(pca1, label="none", habillage= data$Economy_status,
addEllipses=TRUE, ellipse.level=0.95)
ols.data <- data.frame(Life_expectancy=data_dis[,1],pca)
lmodel <- lm(Life_expectancy ~ ., data = ols.data)
summary(lmodel)##
## Call:
## lm(formula = Life_expectancy ~ ., data = ols.data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.81568 -0.23490 -0.01441 0.24825 0.76545
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.654e-16 2.490e-02 0.000 1.000
## PC1 -3.555e-01 1.073e-02 -33.122 < 2e-16 ***
## PC2 1.532e-03 1.703e-02 0.090 0.928
## PC3 -2.739e-01 2.231e-02 -12.277 < 2e-16 ***
## PC4 2.461e-01 2.566e-02 9.590 < 2e-16 ***
## PC5 -1.344e-01 3.285e-02 -4.091 6.60e-05 ***
## PC6 -3.108e-01 3.586e-02 -8.668 3.17e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3332 on 172 degrees of freedom
## Multiple R-squared: 0.8927, Adjusted R-squared: 0.889
## F-statistic: 238.6 on 6 and 172 DF, p-value: < 2.2e-16mean((ols.data$Life_expectancy - predict(lmodel))^2) #mse## [1] 0.1066567sqrt(mean((ols.data$Life_expectancy - predict(lmodel))^2)) ## [1] 0.3265834Factor Analysis
data2## Infant_deaths Under_five_deaths Adult_mortality Alcohol_consumption
## 1 11.1 13.0 105.8240 1.32
## 2 2.7 3.3 57.9025 10.35
## 7 6.6 8.2 223.0000 8.06
## 28 57.0 88.0 340.1265 4.55
## 44 39.7 59.8 261.7065 2.69
## 58 21.6 25.2 95.8155 0.55
## 75 9.6 11.2 89.1875 0.45
## 102 41.3 59.0 218.4575 0.86
## 111 2.2 2.7 53.8970 5.97
## 113 17.4 21.8 124.5470 2.98
## 122 45.2 57.2 434.8210 7.49
## 161 39.6 49.7 248.5950 6.14
## 167 4.3 5.0 160.2370 10.80
## 174 29.2 35.5 154.6040 0.24
## 183 73.0 95.9 260.0235 4.47
## 203 3.1 4.1 163.8720 9.79
## 217 57.7 88.1 242.9655 6.53
## 220 8.1 9.5 202.8000 6.04
## 242 7.7 9.1 85.6715 3.19
## 269 3.2 3.9 56.3370 2.74
## 272 4.6 5.5 67.0000 8.68
## 301 75.7 128.7 363.1670 0.66
## 304 19.3 22.7 148.0870 1.01
## 331 24.8 29.7 162.9175 0.16
## 334 60.0 92.1 270.2885 3.13
## 416 16.5 19.2 146.5195 2.49
## 427 68.4 107.3 262.8710 0.38
## 444 2.3 2.9 53.4415 7.13
## 452 23.2 27.7 175.5640 0.08
## 474 28.8 35.0 161.6170 5.39
## 488 13.9 16.2 110.8405 4.24
## 496 2.5 3.2 82.5385 12.76
## 499 63.2 97.6 242.9535 1.53
## 512 15.2 16.7 154.8235 7.41
## 547 44.7 57.6 198.4490 0.35
## 557 14.2 15.9 144.3625 6.63
## 559 27.4 33.1 209.3720 5.48
## 580 8.3 10.7 82.2730 5.66
## 585 34.0 46.3 255.7810 1.03
## 591 7.5 8.8 58.1365 0.00
## 599 4.7 5.4 65.9695 8.00
## 609 14.3 16.2 141.3000 8.20
## 627 8.5 9.6 75.2050 4.33
## 629 72.6 94.6 513.4755 3.07
## 639 7.8 9.1 87.9740 0.00
## 640 34.9 43.5 177.9465 3.00
## 651 4.0 4.9 165.2330 14.20
## 688 36.4 42.2 189.9280 3.36
## 697 6.5 7.8 130.0025 9.06
## 700 36.7 53.3 294.8580 2.04
## 717 41.0 52.2 196.0530 1.47
## 728 12.7 14.8 151.6085 8.70
## 733 3.4 4.0 58.0775 8.30
## 741 46.2 67.6 294.1870 3.99
## 764 61.3 84.0 332.5830 1.22
## 766 6.9 8.2 136.0675 10.89
## 770 95.1 140.2 397.8705 3.06
## 787 25.6 41.6 178.1065 0.23
## 810 13.3 15.5 182.1595 2.54
## 811 14.6 17.0 114.7010 6.84
## 833 15.0 17.5 109.9420 0.30
## 838 40.9 58.1 239.6670 7.86
## 840 36.1 50.3 238.5125 8.06
## 850 23.3 26.3 124.8970 0.51
## 852 79.3 126.4 356.2145 4.51
## 853 9.3 10.8 148.8890 6.95
## 869 16.6 19.4 212.8410 8.35
## 874 3.0 3.6 73.2830 10.34
## 901 8.4 9.8 68.3620 1.26
## 903 54.4 72.3 227.2735 0.14
## 904 17.3 19.3 168.7145 5.97
## 907 6.5 7.6 68.5765 2.12
## 957 38.9 55.7 311.7215 7.44
## 1000 18.5 23.1 191.5860 5.00
## 1011 62.1 76.0 160.1410 0.04
## 1058 38.8 54.6 244.6325 1.75
## 1064 2.0 2.5 68.8685 8.52
## 1067 53.2 70.4 227.7350 0.00
## 1068 13.2 15.3 174.4925 6.71
## 1117 7.1 8.3 60.3175 1.15
## 1146 2.1 2.6 73.3560 11.49
## 1150 13.4 15.5 132.2455 3.27
## 1157 3.3 4.1 71.7100 10.36
## 1158 67.6 93.2 328.8035 8.11
## 1164 13.0 14.0 99.0935 9.68
## 1197 2.0 2.7 53.5860 8.55
## 1205 10.0 11.4 97.1970 3.57
## 1206 20.2 23.5 70.9135 0.39
## 1225 5.1 6.2 110.5150 10.27
## 1227 34.7 49.4 190.0275 0.19
## 1251 19.5 21.9 136.3935 9.23
## 1262 13.4 15.5 140.0675 4.16
## 1266 32.6 37.5 134.7150 0.92
## 1306 3.0 3.7 64.6875 11.60
## 1320 13.6 15.8 171.2775 6.76
## 1338 37.6 52.6 262.2240 2.05
## 1358 33.3 47.6 315.4730 2.63
## 1481 42.1 61.3 368.1410 3.84
## 1492 5.7 6.6 51.8135 7.37
## 1503 35.2 48.9 223.6080 1.65
## 1531 3.3 4.0 100.8610 8.49
## 1536 3.8 4.4 70.7555 6.68
## 1559 25.4 31.3 184.5200 3.15
## 1566 3.2 3.7 61.0195 10.81
## 1588 4.2 4.9 90.2285 9.64
## 1604 19.9 22.3 165.7935 5.37
## 1614 3.7 4.3 49.3840 9.62
## 1620 23.7 28.3 163.8125 1.65
## 1624 6.7 7.8 56.2695 1.03
## 1629 55.0 82.7 203.5835 0.00
## 1707 46.1 60.7 221.5195 0.03
## 1710 46.9 67.7 302.8220 3.50
## 1713 10.6 11.9 182.1110 3.33
## 1716 5.4 6.3 114.3280 7.20
## 1722 19.0 22.3 145.3510 5.21
## 1732 24.2 28.9 164.8710 1.59
## 1785 5.4 6.3 96.0670 4.90
## 1801 8.8 10.6 88.0930 0.67
## 1810 3.8 4.5 69.3335 9.59
## 1820 51.8 93.8 249.0860 0.12
## 1824 12.6 14.1 125.4875 4.04
## 1844 31.0 38.1 129.7530 0.01
## 1875 83.6 134.3 308.3030 0.00
## 1882 17.3 19.3 140.8150 2.59
## 1905 7.6 8.9 105.6850 6.00
## 1948 6.7 7.9 88.8665 7.89
## 1950 3.3 3.9 71.3120 11.06
## 1976 64.4 88.3 241.0125 3.18
## 1984 3.5 4.1 67.1710 9.42
## 1989 34.6 47.7 203.5740 6.31
## 2022 12.8 14.5 144.3615 2.83
## 2077 40.2 51.0 225.4075 1.36
## 2081 2.2 2.7 50.9615 1.82
## 2118 13.3 15.5 81.8615 0.01
## 2120 4.2 4.9 113.6690 10.47
## 2127 3.0 3.5 52.9595 7.14
## 2128 4.5 5.7 89.2395 4.65
## 2146 12.2 15.7 124.0700 5.68
## 2148 23.6 28.2 131.2085 1.42
## 2178 27.3 31.8 175.6540 3.34
## 2182 4.2 5.1 131.7765 10.95
## 2235 87.9 123.3 411.0745 0.90
## 2279 3.3 3.9 61.7325 9.68
## 2281 19.8 23.3 149.5290 0.18
## 2291 9.4 10.5 156.2355 6.95
## 2322 12.0 14.0 158.5890 9.27
## 2324 18.2 20.3 170.1290 4.75
## 2325 2.3 2.8 54.3930 11.37
## 2339 11.4 13.3 134.7895 0.01
## 2357 5.8 6.8 107.3770 8.78
## 2368 10.2 11.5 117.1895 8.49
## 2379 27.4 33.1 208.0030 0.04
## 2396 2.4 2.9 51.6435 9.59
## 2405 16.7 19.5 125.1490 4.54
## 2410 42.1 53.8 195.6250 7.09
## 2443 1.8 2.3 55.3590 7.66
## 2449 50.8 75.9 271.7090 1.36
## 2469 2.4 3.1 116.3510 16.72
## 2496 23.4 29.6 199.7365 4.52
## 2519 7.7 9.2 128.6030 9.45
## 2526 52.8 69.9 243.6235 2.78
## 2582 65.7 90.8 396.4580 1.54
## 2618 59.6 100.9 257.9580 7.03
## 2621 13.2 15.4 123.9060 3.69
## 2642 42.8 50.2 149.7365 0.41
## 2651 20.6 24.4 185.8580 2.63
## 2662 66.8 108.3 267.5905 0.62
## 2680 15.9 18.6 111.9490 2.10
## 2702 7.5 8.7 109.1795 2.72
## 2711 43.2 62.4 224.4230 0.76
## 2713 3.2 4.2 75.4835 11.87
## 2728 6.9 8.1 121.7230 0.55
## 2738 10.7 12.4 134.0135 0.23
## 2753 28.6 36.3 351.3925 7.20
## 2754 14.8 17.2 91.3430 1.50
## 2821 16.4 19.1 141.5540 6.21
## 2841 54.6 65.8 251.7490 0.32
## 2847 16.6 19.4 148.4805 3.72
## 2849 6.5 7.6 66.6840 1.53
## Hepatitis_B Measles BMI Polio Diphtheria Incidents_HIV GDP_per_capita
## 1 97 65 27.8 97 97 0.08 11006
## 2 97 94 26.0 97 97 0.09 25742
## 7 97 97 26.2 97 97 0.08 9313
## 28 84 64 24.3 77 84 1.12 1383
## 44 97 64 23.9 96 97 0.96 661
## 58 95 99 25.5 95 95 0.05 4178
## 75 99 98 26.3 99 99 0.05 18445
## 102 69 64 21.3 68 69 0.24 467
## 111 88 91 26.6 95 95 0.04 74356
## 113 97 65 21.7 97 97 0.12 2582
## 122 90 83 26.8 84 90 14.30 3680
## 161 95 80 24.3 96 95 5.81 6403
## 167 94 92 26.6 94 95 0.29 13786
## 174 91 65 22.4 90 91 0.17 902
## 183 81 64 21.9 78 81 0.35 497
## 203 99 99 26.6 99 99 0.22 5967
## 217 64 64 23.2 62 64 0.89 3128
## 220 22 57 26.5 51 23 0.23 2125
## 242 92 90 27.3 92 92 0.19 11643
## 269 96 97 27.2 95 95 0.08 35808
## 272 92 87 28.0 92 92 0.03 38631
## 301 46 64 21.9 52 46 0.42 776
## 304 98 65 26.2 85 98 0.17 2167
## 331 56 76 28.6 72 58 0.13 4688
## 334 87 64 23.4 83 87 1.58 603
## 416 97 83 26.7 98 97 0.07 2302
## 427 54 64 22.9 47 54 0.74 769
## 444 67 95 26.0 98 98 0.08 51545
## 452 78 31 23.0 85 78 0.15 3332
## 474 81 83 26.4 87 85 0.38 6922
## 488 82 96 27.9 87 87 0.16 9617
## 496 97 99 27.0 97 97 0.08 17830
## 499 82 83 23.5 72 82 0.33 1077
## 512 98 83 27.1 97 98 0.40 7207
## 547 82 76 30.0 80 78 0.17 1535
## 557 96 80 26.5 98 96 0.24 8814
## 559 95 95 26.3 92 95 0.59 5577
## 580 99 99 23.7 99 99 0.10 8016
## 585 95 88 20.7 95 95 0.10 9011
## 591 99 96 29.5 99 99 0.13 29870
## 599 55 86 26.9 91 91 0.10 43596
## 609 92 89 26.9 99 92 0.40 9097
## 627 99 98 26.6 99 99 0.03 3953
## 629 93 82 24.9 85 93 10.00 1146
## 639 98 96 28.4 97 98 0.13 20628
## 640 87 69 21.7 86 87 0.06 1606
## 651 94 92 26.4 93 93 0.09 14264
## 688 99 99 26.4 99 99 0.08 6433
## 697 99 84 26.6 86 99 0.20 14285
## 700 88 64 22.8 88 88 2.59 381
## 717 89 78 22.6 89 89 0.28 1197
## 728 98 98 26.6 97 97 3.50 15158
## 733 94 92 25.5 95 95 0.04 45193
## 741 94 65 21.6 94 94 0.27 306
## 764 88 64 22.7 88 80 3.50 590
## 766 92 87 26.4 91 91 0.03 7075
## 770 86 60 22.7 86 86 0.85 588
## 787 41 47 28.2 50 41 0.13 979
## 810 91 88 27.6 92 91 0.18 3706
## 811 73 92 26.8 72 73 0.40 13630
## 833 99 96 28.9 99 99 0.13 4164
## 838 98 64 23.1 96 98 2.01 948
## 840 80 64 25.2 79 80 1.09 7385
## 850 96 98 26.9 98 96 0.05 5500
## 852 49 64 23.2 42 49 0.58 2687
## 853 99 95 24.3 99 99 0.16 5840
## 869 99 98 26.1 99 99 0.01 3875
## 874 98 95 25.7 98 98 0.12 19250
## 901 99 99 25.3 99 99 0.17 9033
## 903 91 64 24.3 92 91 0.01 1243
## 904 90 79 27.5 88 96 0.40 18384
## 907 99 99 28.4 99 99 0.13 38663
## 957 78 64 22.4 85 78 2.08 847
## 1000 96 76 24.7 96 96 0.15 1585
## 1011 72 54 23.9 72 72 0.13 1357
## 1058 88 63 23.9 88 88 0.84 1774
## 1064 88 92 25.9 97 97 0.08 42802
## 1067 65 42 23.3 67 65 0.03 556
## 1068 94 95 28.9 94 94 0.40 4805
## 1117 81 63 27.5 81 81 0.04 7643
## 1146 88 96 26.5 95 95 0.01 20890
## 1150 91 83 27.6 91 91 0.47 4908
## 1157 98 85 26.1 99 99 0.08 41008
## 1158 40 64 23.9 37 16 4.20 11283
## 1164 97 89 27.7 97 97 0.28 16559
## 1197 83 93 22.7 99 96 0.17 34961
## 1205 92 97 26.7 92 91 0.08 4862
## 1206 99 95 25.9 99 99 0.03 2875
## 1225 96 97 26.4 96 96 0.02 16342
## 1227 89 54 22.9 85 89 0.10 1219
## 1251 99 83 29.8 99 99 0.40 10094
## 1262 91 86 26.1 91 91 0.19 6176
## 1266 96 94 25.9 96 96 0.11 978
## 1306 93 88 25.5 93 93 0.08 44196
## 1320 88 92 27.0 88 87 0.36 2732
## 1338 80 64 23.1 80 80 2.04 2449
## 1358 92 64 24.2 92 92 4.58 4897
## 1481 87 64 23.8 88 87 3.86 1445
## 1492 95 91 27.1 97 97 0.08 24922
## 1503 89 28 23.3 83 89 1.15 1465
## 1531 82 94 26.5 89 89 0.03 6517
## 1536 96 83 27.1 99 99 0.06 18084
## 1559 99 83 26.4 99 99 0.15 3036
## 1566 95 86 27.4 95 95 0.07 62012
## 1588 94 96 27.3 94 94 0.02 11933
## 1604 97 65 26.5 97 97 0.12 1121
## 1614 88 87 25.2 96 97 0.05 84776
## 1620 74 83 26.5 69 74 0.03 3995
## 1624 99 91 29.1 99 99 0.06 63039
## 1629 73 64 24.9 67 73 0.15 1524
## 1707 69 95 23.7 63 69 0.03 1602
## 1710 90 47 22.5 90 90 4.48 1338
## 1713 98 98 26.3 98 98 0.14 10511
## 1716 94 86 26.0 95 95 0.02 5589
## 1722 93 72 26.6 93 93 0.14 5414
## 1732 78 65 29.6 71 72 0.17 2907
## 1785 82 88 25.7 74 82 0.08 4730
## 1801 99 97 27.0 99 99 0.10 31164
## 1810 88 86 27.1 96 96 0.08 45405
## 1820 65 64 21.8 83 65 0.06 484
## 1824 94 97 26.3 96 94 0.09 3607
## 1844 97 90 21.6 98 97 0.01 1248
## 1875 42 64 23.1 47 42 0.13 386
## 1882 99 99 26.7 99 99 0.14 2754
## 1905 95 93 27.3 95 95 0.24 15614
## 1948 97 89 27.9 96 96 0.19 13495
## 1950 88 93 26.5 92 95 0.03 41103
## 1976 52 64 24.0 65 52 3.50 722
## 1984 88 80 25.3 93 93 0.03 53255
## 1989 98 87 22.0 99 98 0.59 751
## 2022 97 96 25.2 98 97 0.70 9260
## 2077 67 65 25.5 51 73 0.41 2679
## 2081 96 90 23.6 96 96 0.07 55647
## 2118 98 65 26.1 98 98 0.04 5201
## 2120 96 94 26.6 92 98 0.08 12578
## 2127 93 83 25.6 93 93 0.06 30242
## 2128 99 99 25.6 99 99 0.16 7694
## 2146 90 63 26.5 88 90 0.13 6229
## 2148 64 65 26.1 80 64 0.17 2696
## 2178 89 61 22.1 92 89 0.10 1163
## 2182 88 99 27.2 99 99 0.08 12721
## 2235 47 64 22.8 51 47 1.12 377
## 2279 93 93 27.1 93 93 0.04 56707
## 2281 93 64 29.5 93 93 0.13 3563
## 2291 94 91 27.5 91 94 0.14 4014
## 2322 95 83 27.9 95 95 0.34 31699
## 2324 89 21 26.5 78 89 0.47 9168
## 2325 94 86 26.3 99 99 0.10 105462
## 2339 97 97 28.0 97 97 0.08 7590
## 2357 92 86 28.8 93 95 0.12 56763
## 2368 94 87 27.6 93 94 0.13 13789
## 2379 99 94 23.8 98 99 0.13 2753
## 2396 97 88 26.8 97 97 0.06 23408
## 2405 96 95 24.5 93 93 0.26 3043
## 2410 89 65 22.8 89 89 0.15 2140
## 2443 88 94 26.2 92 92 0.05 52952
## 2449 88 64 23.5 82 88 0.72 571
## 2469 91 92 26.4 93 93 0.08 17402
## 2496 75 57 23.1 79 60 0.10 3001
## 2519 90 80 26.7 89 89 0.04 8969
## 2526 64 83 25.2 64 60 0.67 1387
## 2582 83 64 23.7 81 83 0.63 1973
## 2618 91 50 22.1 91 91 0.16 653
## 2621 78 76 27.1 84 78 0.16 6124
## 2642 76 64 21.2 75 76 0.10 1333
## 2651 99 94 27.6 99 99 0.12 5391
## 2662 64 64 22.9 67 64 0.39 751
## 2680 59 55 32.1 78 66 0.17 4074
## 2702 99 99 23.0 99 99 0.01 3844
## 2711 77 64 20.5 75 77 0.19 641
## 2713 86 79 25.0 97 98 0.09 36653
## 2728 99 99 25.6 99 99 0.14 9955
## 2738 78 99 32.1 96 78 0.17 4336
## 2753 75 59 27.2 85 75 6.91 6260
## 2754 98 98 26.3 98 98 0.04 4095
## 2821 87 83 26.7 87 87 0.40 17318
## 2841 84 82 24.0 84 84 0.22 2653
## 2847 98 83 27.2 99 98 0.11 2050
## 2849 98 99 24.8 98 98 0.05 22634
## Population_mln Thinness_ten_nineteen_years Thinness_five_nine_years
## 1 78.53 4.9 4.8
## 2 46.44 0.6 0.5
## 7 144.10 2.3 2.3
## 28 23.30 5.6 5.5
## 44 2.09 7.3 7.2
## 58 39.73 6.0 5.8
## 75 4.27 7.1 6.9
## 102 24.23 7.1 7.1
## 111 5.19 0.8 0.7
## 113 92.68 14.2 14.5
## 122 1.10 4.0 4.1
## 161 2.12 6.4 6.1
## 167 1.98 2.2 2.1
## 174 27.02 15.7 16.1
## 183 76.24 9.5 9.3
## 203 9.46 1.9 2.0
## 217 27.88 8.3 8.2
## 220 45.15 2.3 2.4
## 242 4.85 1.7 1.7
## 269 8.38 1.2 1.1
## 272 4.61 0.4 0.3
## 301 14.11 8.5 8.4
## 304 0.60 1.1 1.2
## 331 35.57 5.3 5.1
## 334 1.74 7.1 7.0
## 416 9.11 2.1 2.1
## 427 11.43 7.3 7.3
## 444 9.80 1.5 1.4
## 452 258.38 1.4 1.2
## 474 10.28 3.3 3.2
## 488 121.86 1.5 1.5
## 496 10.55 1.8 1.8
## 499 10.58 6.9 6.8
## 512 0.11 3.5 3.4
## 547 0.11 0.1 0.1
## 557 204.47 2.7 2.6
## 559 0.77 5.5 5.3
## 580 1379.86 3.6 2.9
## 585 0.35 8.4 8.2
## 591 3.84 3.5 3.4
## 599 35.70 0.6 0.5
## 609 0.11 3.8 3.8
## 627 2.88 1.2 1.3
## 629 2.06 5.5 5.3
## 639 31.72 7.8 7.6
## 640 1310.15 26.7 27.3
## 651 2.90 2.6 2.6
## 688 5.57 3.3 3.3
## 697 0.09 3.3 3.3
## 700 16.75 6.4 6.2
## 717 52.68 12.8 13.0
## 728 0.09 5.7 6.0
## 733 16.94 1.0 0.9
## 741 10.16 7.3 7.2
## 764 27.04 3.6 3.5
## 766 7.18 1.9 1.8
## 770 7.17 7.4 7.3
## 787 18.00 6.3 6.1
## 810 6.33 1.6 1.5
## 811 3.97 1.9 1.8
## 833 9.27 4.0 4.0
## 838 51.48 6.7 6.5
## 840 1.95 6.1 5.9
## 850 9.65 2.8 2.9
## 852 181.14 9.8 9.7
## 853 68.71 7.7 7.7
## 869 3.00 2.2 2.3
## 874 10.36 0.7 0.5
## 901 0.45 13.6 13.6
## 903 0.78 6.7 6.5
## 904 1.37 5.7 5.9
## 907 9.26 5.3 5.1
## 957 38.23 5.6 5.6
## 1000 0.20 5.5 5.3
## 1011 199.43 19.2 19.6
## 1058 27.85 6.2 6.1
## 1064 5.48 0.9 0.8
## 1067 34.41 17.2 17.3
## 1068 0.36 3.5 3.4
## 1117 6.53 4.9 4.9
## 1146 2.06 1.4 1.3
## 1150 2.89 1.8 1.7
## 1157 11.27 1.0 1.0
## 1158 1.17 8.4 8.3
## 1164 0.29 3.8 3.7
## 1197 127.14 2.1 1.8
## 1205 2.07 2.1 2.1
## 1206 34.66 6.4 6.2
## 1225 5.42 1.2 1.2
## 1227 14.58 9.5 9.3
## 1251 0.18 4.3 4.3
## 1262 47.52 2.1 1.9
## 1266 8.45 3.6 3.7
## 1306 8.64 1.9 2.1
## 1320 2.83 2.7 2.8
## 1338 4.86 7.5 7.1
## 1358 2.31 8.2 8.1
## 1481 13.81 5.6 5.5
## 1492 0.45 0.8 0.8
## 1503 47.88 7.8 7.6
## 1531 0.62 1.8 1.8
## 1536 10.82 0.8 0.7
## 1559 10.87 1.2 1.1
## 1566 4.70 0.3 0.2
## 1588 4.20 1.5 1.4
## 1604 5.96 3.3 3.4
## 1614 8.28 0.4 0.3
## 1620 15.57 1.2 1.2
## 1624 2.57 5.2 4.9
## 1629 4.05 7.8 7.5
## 1707 26.50 13.6 13.4
## 1710 15.88 6.3 6.1
## 1713 17.54 2.4 2.5
## 1716 7.10 2.0 2.0
## 1722 6.69 2.0 1.9
## 1732 0.11 0.2 0.2
## 1785 3.43 2.3 2.3
## 1801 0.41 5.7 5.1
## 1810 65.12 0.8 0.6
## 1820 20.00 9.6 9.4
## 1824 2.93 2.1 2.2
## 1844 156.26 17.9 18.3
## 1875 13.80 6.6 6.4
## 1882 31.30 3.0 3.1
## 1905 3.41 1.5 1.4
## 1948 17.97 0.8 0.8
## 1950 81.69 1.1 1.1
## 1976 4.47 6.5 6.4
## 1984 5.68 1.1 0.9
## 1989 11.37 5.7 5.7
## 2022 1.26 6.9 6.8
## 2077 8.11 1.3 1.3
## 2081 5.54 2.2 2.2
## 2118 78.49 8.5 8.6
## 2120 37.99 1.9 2.0
## 2127 60.73 0.6 0.6
## 2128 11.32 3.5 3.3
## 2146 30.47 1.1 1.1
## 2148 0.27 1.5 1.4
## 2178 15.52 1.9 1.9
## 2182 9.84 1.6 1.6
## 2235 4.49 8.2 8.2
## 2279 23.82 0.6 0.6
## 2281 92.44 2.8 2.8
## 2291 3.73 2.7 2.8
## 2322 0.37 2.5 2.5
## 2324 0.56 3.5 3.5
## 2325 0.57 1.0 0.9
## 2339 6.42 5.8 5.5
## 2357 320.74 0.8 0.6
## 2368 43.13 1.0 0.9
## 2379 0.73 15.4 16.0
## 2396 1.16 1.0 1.0
## 2405 0.52 6.6 6.6
## 2410 6.74 8.8 8.9
## 2443 0.33 1.0 0.9
## 2449 7.32 6.5 6.2
## 2469 1.32 1.9 1.9
## 2496 102.11 1.0 9.7
## 2519 19.82 2.5 2.7
## 2526 10.70 3.9 3.9
## 2582 23.23 5.5 5.5
## 2618 18.11 8.0 7.5
## 2621 16.21 1.2 1.1
## 2642 1.20 1.9 11.1
## 2651 0.87 4.0 3.7
## 2662 17.44 7.7 7.5
## 2680 0.19 0.2 0.1
## 2702 20.97 15.1 15.0
## 2711 100.84 1.4 1.2
## 2713 66.55 0.7 0.6
## 2728 30.27 7.5 7.3
## 2738 0.10 0.1 0.1
## 2753 55.39 4.4 5.3
## 2754 11.18 6.5 6.4
## 2821 30.08 1.6 1.5
## 2841 0.91 5.6 5.4
## 2847 6.22 1.8 1.7
## 2849 1.37 6.2 6.1
## Schooling Life_expectancy
## 1 7.8 76.5
## 2 9.7 82.8
## 7 12.0 71.2
## 28 6.1 57.6
## 44 3.4 60.9
## 58 7.9 76.1
## 75 9.5 76.9
## 102 6.1 65.5
## 111 12.5 82.3
## 113 8.0 75.1
## 122 6.5 55.4
## 161 9.2 67.3
## 167 12.8 74.5
## 174 4.7 69.5
## 183 6.4 59.3
## 203 12.2 73.6
## 217 5.0 59.4
## 220 11.3 71.2
## 242 8.8 79.6
## 269 13.0 82.1
## 272 12.4 81.5
## 301 2.3 53.1
## 304 5.4 72.2
## 331 6.6 69.9
## 334 2.9 57.0
## 416 6.3 74.5
## 427 2.6 59.6
## 444 12.4 82.2
## 452 7.9 70.8
## 474 7.8 73.2
## 488 8.6 74.9
## 496 12.7 78.6
## 499 3.5 60.6
## 512 8.6 72.1
## 547 7.9 67.3
## 557 7.6 75.0
## 559 8.4 69.3
## 580 7.7 75.9
## 585 3.9 64.7
## 591 7.1 75.1
## 599 13.1 81.9
## 609 8.7 72.4
## 627 9.7 78.0
## 629 6.1 51.0
## 639 9.5 74.7
## 640 6.3 68.6
## 651 13.0 74.3
## 688 9.8 67.7
## 697 9.2 76.5
## 700 4.4 62.0
## 717 4.9 65.8
## 728 9.5 74.3
## 733 12.1 81.5
## 741 2.9 60.1
## 764 3.5 57.2
## 766 11.8 74.6
## 770 3.4 52.9
## 787 5.1 69.9
## 810 6.6 72.4
## 811 9.9 77.8
## 833 10.3 74.1
## 838 5.8 63.1
## 840 8.1 64.9
## 850 10.7 72.3
## 852 6.0 53.1
## 853 7.6 76.1
## 869 10.1 69.1
## 874 9.1 81.1
## 901 6.3 77.7
## 903 4.8 63.5
## 904 10.8 72.9
## 907 10.6 77.3
## 957 5.7 61.4
## 1000 5.6 69.4
## 1011 5.1 66.6
## 1058 6.9 62.8
## 1064 12.4 81.5
## 1067 3.6 63.4
## 1068 10.5 74.0
## 1117 8.5 78.8
## 1146 12.0 80.8
## 1150 9.6 74.1
## 1157 11.7 81.0
## 1158 5.5 57.4
## 1164 10.5 78.8
## 1197 12.5 83.8
## 1205 9.6 75.4
## 1206 5.0 75.7
## 1225 12.5 76.6
## 1227 2.9 66.7
## 1251 8.9 75.6
## 1262 8.1 76.5
## 1266 10.5 70.1
## 1306 12.1 81.2
## 1320 11.6 71.5
## 1338 6.3 63.1
## 1358 6.7 62.1
## 1481 8.2 59.5
## 1492 11.2 81.9
## 1503 6.3 64.8
## 1531 11.3 76.4
## 1536 10.6 81.0
## 1559 8.7 70.3
## 1566 12.3 81.5
## 1588 11.2 77.3
## 1604 10.8 70.7
## 1614 13.4 82.9
## 1620 6.3 73.3
## 1624 9.8 79.8
## 1629 4.3 63.9
## 1707 3.0 66.1
## 1710 6.9 61.7
## 1713 11.7 72.0
## 1716 11.0 75.3
## 1722 8.5 73.7
## 1732 8.0 67.3
## 1785 9.0 76.9
## 1801 9.0 75.3
## 1810 12.8 81.0
## 1820 1.8 60.6
## 1824 11.6 74.5
## 1844 5.2 71.5
## 1875 2.1 55.9
## 1882 11.4 70.9
## 1905 8.7 77.4
## 1948 10.3 79.6
## 1950 14.1 80.6
## 1976 4.4 62.3
## 1984 12.5 80.7
## 1989 4.0 67.5
## 2022 9.1 74.4
## 2077 4.3 63.5
## 2081 11.5 82.7
## 2118 9.8 75.8
## 2120 12.1 77.5
## 2127 10.2 82.5
## 2128 11.4 78.6
## 2146 9.1 75.8
## 2148 6.8 69.9
## 2178 4.7 68.6
## 2182 11.8 75.6
## 2235 4.2 50.9
## 2279 12.8 82.4
## 2281 7.1 71.3
## 2291 12.7 73.0
## 2322 11.1 73.1
## 2324 8.4 71.2
## 2325 12.0 82.3
## 2339 7.3 72.1
## 2357 13.3 78.7
## 2368 9.8 76.1
## 2379 3.1 70.4
## 2396 11.9 80.4
## 2405 5.9 72.1
## 2410 5.1 66.5
## 2443 12.2 82.5
## 2449 4.7 59.9
## 2469 12.7 77.6
## 2496 9.3 70.6
## 2519 10.9 74.9
## 2526 5.2 62.5
## 2582 5.0 56.1
## 2618 1.4 59.9
## 2621 8.4 76.1
## 2642 4.5 68.5
## 2651 10.8 67.1
## 2662 2.3 57.5
## 2680 10.3 72.7
## 2702 10.9 76.3
## 2711 2.6 65.0
## 2713 11.5 82.3
## 2728 10.2 75.5
## 2738 11.2 70.5
## 2753 10.1 62.6
## 2754 7.0 75.9
## 2821 10.1 72.6
## 2841 4.1 64.1
## 2847 6.5 73.6
## 2849 9.3 76.8cm <- cor(data2, method="pearson")
corrplot::corrplot(cm, method= "number", order = "hclust")
KMO(r=cm)## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = cm)
## Overall MSA = 0.84
## MSA for each item =
## Infant_deaths Under_five_deaths
## 0.86 0.83
## Adult_mortality Alcohol_consumption
## 0.84 0.83
## Hepatitis_B Measles
## 0.82 0.97
## BMI Polio
## 0.87 0.93
## Diphtheria Incidents_HIV
## 0.80 0.70
## GDP_per_capita Population_mln
## 0.88 0.85
## Thinness_ten_nineteen_years Thinness_five_nine_years
## 0.73 0.72
## Schooling Life_expectancy
## 0.92 0.87print(cortest.bartlett(cm,nrow(data2)))## $chisq
## [1] 3781.936
##
## $p.value
## [1] 0
##
## $df
## [1] 120parallel <- fa.parallel(data2, fm = "minres", fa = "fa")
## Parallel analysis suggests that the number of factors = 3 and the number of components = NAfactanal(data2, factors = 3, ,lower=0.01225)$PVAL## objective
## 9.683779e-78factanal(data2, factors =7,lower=0.0122222225 )$PVAL## objective
## 0.0002878897f<-factanal(data2, factors = 7,lower=0.0122222225)
f##
## Call:
## factanal(x = data2, factors = 7, lower = 0.0122222225)
##
## Uniquenesses:
## Infant_deaths Under_five_deaths
## 0.012 0.012
## Adult_mortality Alcohol_consumption
## 0.012 0.421
## Hepatitis_B Measles
## 0.072 0.554
## BMI Polio
## 0.012 0.103
## Diphtheria Incidents_HIV
## 0.016 0.478
## GDP_per_capita Population_mln
## 0.348 0.871
## Thinness_ten_nineteen_years Thinness_five_nine_years
## 0.012 0.012
## Schooling Life_expectancy
## 0.173 0.021
##
## Loadings:
## Factor1 Factor2 Factor3 Factor4 Factor5 Factor6
## Infant_deaths -0.418 -0.433 0.433 0.146 -0.297 0.574
## Under_five_deaths -0.440 -0.402 0.414 0.132 -0.320 0.586
## Adult_mortality -0.301 -0.373 0.796 -0.245 0.249
## Alcohol_consumption 0.151 0.680 -0.229 -0.190
## Hepatitis_B 0.955
## Measles 0.443 0.329 -0.224 0.262 -0.123
## BMI 0.133 0.149 -0.159 -0.409 0.855 -0.157
## Polio 0.893 0.204 -0.144 -0.166
## Diphtheria 0.965 0.181 -0.117
## Incidents_HIV 0.721
## GDP_per_capita 0.133 0.724 -0.297 -0.112
## Population_mln 0.342
## Thinness_ten_nineteen_years -0.315 0.134 0.903 0.201
## Thinness_five_nine_years -0.323 0.125 0.896 -0.131 0.154
## Schooling 0.268 0.657 -0.174 -0.241 0.343 -0.339
## Life_expectancy 0.349 0.524 -0.623 0.243 -0.353
## Factor7
## Infant_deaths
## Under_five_deaths
## Adult_mortality
## Alcohol_consumption
## Hepatitis_B
## Measles
## BMI
## Polio
## Diphtheria
## Incidents_HIV
## GDP_per_capita
## Population_mln
## Thinness_ten_nineteen_years
## Thinness_five_nine_years 0.122
## Schooling
## Life_expectancy
##
## Factor1 Factor2 Factor3 Factor4 Factor5 Factor6 Factor7
## SS loadings 3.564 2.592 2.175 2.086 1.277 1.157 0.025
## Proportion Var 0.223 0.162 0.136 0.130 0.080 0.072 0.002
## Cumulative Var 0.223 0.385 0.521 0.651 0.731 0.803 0.805
##
## Test of the hypothesis that 7 factors are sufficient.
## The chi square statistic is 62.63 on 29 degrees of freedom.
## The p-value is 0.000288load <- f$loadings[,1:2]
plot(load,type="n") # set up plot
text(load,labels=names(data2),cex=.7)
names(f$loadings[,1])[abs(f$loadings[,1])>0.4]## [1] "Infant_deaths" "Under_five_deaths" "Hepatitis_B"
## [4] "Measles" "Polio" "Diphtheria"f1<-data2[,names(f$loadings[,1])[abs(f$loadings[,1])>0.4]]summary(alpha(f1, check.keys=TRUE))## Number of categories should be increased in order to count frequencies.## Warning in alpha(f1, check.keys = TRUE): Some items were negatively correlated with the first principal component and were automatically reversed.
## This is indicated by a negative sign for the variable name.##
## Reliability analysis
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.89 0.92 0.96 0.67 12 0.011 95 16 0.59scores<-factanal(data2, factors = 7,lower=0.0122222225,scores="regression")$scores
head(scores)## Factor1 Factor2 Factor3 Factor4 Factor5 Factor6
## 1 0.638322681 -0.6669749 -0.583670 0.1180494 1.09915803 -0.03638192
## 2 0.380428326 1.0250218 -1.001402 -0.5856033 -0.48752162 -0.01020663
## 7 0.658902252 0.4200210 1.672434 -0.3090451 0.02366873 -1.58966325
## 28 -0.001745963 -0.3580919 1.777462 -0.3923677 -0.27800581 1.23305421
## 44 1.010716464 -1.4200139 0.841323 0.0809353 -0.58536651 0.24317847
## 58 0.507667521 -0.3947061 -1.120713 0.3166194 -0.01042125 0.52130319
## Factor7
## 1 0.023789785
## 2 -0.002407151
## 7 -0.342100665
## 28 -0.193267846
## 44 -0.452529575
## 58 0.109165559cm <- cor(data2, method="pearson")
corrplot::corrplot(cm, method= "number", order = "hclust")